Engine is knocking and shaking whole car; have ruled out ignition coil by tests; frequently stalls when idle; acts as if only running on 4-5 cylinders instead of 6

Possible IAC, idle control valve, trouble. Could be dirty. Did you add the sea foam through the throttle body or fuel tank? Also could be the electric control module.

Most cars use a very similar setup so being a cadillac shouldn't make too much difference. Your wire fix should Not be used for a few days as you could be doing more damage to the vehicle.
Check the obvious, simple stuff first. When was the car last serviced? A clogged or dirty air/fuel filter can affect the engine more than you think. Look in the coolant tank to see if there is oil floating on the top and in the oil filler hole for a 'mayonnaise' like build up. These are clues to a blown head gasket.
Do you have any warning lights on the dashboard? If you have access to an OBD2 scanner you can check for Trouble Codes to see if it is a sensor causing the issue.
Another possible cause is a vacuum leak somewhere in the system. As a 2002 car vacuum pipes do get old and start leaking.
Your next fix is to take it to a good mechanic and let them look at it as they might spot something you missed.

Unplugging the the fuel injector's connector had an effect on the engine's idle/stalls (all 4 fuel injectors): This test result tells you that the misfire is either intermittent (not present at this time) or that the problem (causing the rough idle) is affecting all 4 cylinders evenly.
This test result also rules out your Toyota having a bad fuel injector.

I own a 2000 avalon and had a similar issue, rough idle especially when stopped, car felt like it was going to stall. I had a couple error codes which included one of the o2 sensors and knock sensors. I replaced the pcv valve , and o2 sensor, both easy fixes, but tue knock sensor is in the top half of the engine. Cost me 500 bucks to replace, install knock sensor at shop. After knock sensor was replaced and other o2 sensor replaced, no more idle issues. What happens if an o2 sensor on one of

. The answer is to replace all the spark plugs and wires. Even if the plug appears fine to the ***** eye, and the wire has no visible damage, there could be problems with it that cause it not to fire properly. if you have coils on it, check them also.
An ignition coil that is failing will still provide current to the plugs, but it might not be enough for a full spark and the car will run sluggishly. If the current being provided by the coil isn't consistent, the car will run rough. make sure your getting good spark from coil first. good-day !

po700 code just means you have codes
P0351-IGNITION COIL #1 PRIMARY CIRCUIT

WHEN MONITORED
With battery voltage greater than 8 volts during engine cranking or greater than 13 volts with engine running. Engine RPM less than 3000. No coil in dwell during test.

SET CONDITION
Peak current is not achieved with battery based dwell plus 1.5 msec of diagnostic offset. It takes less than 3 seconds during cranking or up to 6 seconds while running to set.

POSSIBLE CAUSES
- Ignition coil
- Intermittent condition
- ASD relay output circuit
- Ignition coil driver circuit open
- Ignition coil driver circuit shorted to ground
- PCM

P0352-IGNITION COIL #2 PRIMARY CIRCUIT

TEST NOTE
This symptom is diagnosed using the test P0351-IGNITION COIL #1 PRIMARY CIRCUIT.

WHEN MONITORED
With battery voltage greater than 8 volts during engine cranking or greater than 13 volts with engine running. Engine RPM less than 3000. No coil in dwell during test.

SET CONDITION
Peak current is not achieved with battery based dwell plus 1.5 msec of diagnostic offset. It takes less than 3 seconds during cranking or up to 6 seconds while running to set.

POSSIBLE CAUSES
- Ignition coil
- Intermittent condition
- ASD relay output circuit
- Ignition coil driver circuit open
- Ignition coil driver circuit shorted to ground
- PCM
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What I see the most often is a stalled engine with a loss of spark when driving. Once the engine cools off it will sometimes start and run fine for a short while then do the same thing again. Often, but not always, the pickup up coil or ignition module [both are under the distributor cap] have to heat up quite a bit before they will act up. I replace about 10 ignition modules for every one pickup coil but either one can cause the same identical stalling problem. I keep a few known good modules around as test units so I can just replace a suspected bad module and road test it to see if it works. Another thing that can go wrong in these distributors are the magnets built into the pole piece. A weak or cracked magnet can cause all kinds of odd problems such as stalling when placed in reverse, misfires over 1,000 rpm, etc. Worn bushings in the distributor can also cause problems. As far as a specific test you can do to see which part is failing? I wish there was a relaible one. I've tried using a lab scope and module testers to diganose the culprit but you have to catch the problem as it's happening for those tests to be accurate.

I had a problem with starts on my 98 sc2, did it twice only, but it would start up, shake a bit then shut down like it wasn't getting fuel, or a wrong mixture. Replaced the coolant temperature sensor and starts / idles like new now... goodluck

Here is the first half of the codes look till you find the one you have
111 System PASS.
112 ACT sensor circuit grounded.
113 ACT sensor circuit open.
114 ACT sensor is out of Self-Test.
116 ECT sensor is out of Self-Test.
117 ECT sensor circuit grounded.
118 ECT sensor circuit open.
121 TP sensor is out of Self-Test.
122 TP sensor input is less than Self-Test minimum.
123 TP sensor input is greater than Self-Test maximum.
124 TP sensor input voltage is greater than expected.
125 TP sensor input voltage is less than expected.
128 MAP vacuum hose damaged or disconnected.
129 Insufficient MAF input.
136 HEGO sensor circuit indicates system lean (Right HEGO).
137 HEGO sensor circuit indicates system rich (Right HEGO).
139 No HEGO switching (Front Side).
141 Fuel system indicates lean.
144 No HEGO switching (Left Side).
157 MAF sensor circuit open.
158 MAF sensor shorted to power.
159 MAF sensor is out of Self-Test.
167 Insufficient TP input change.
171 Lack of HEGO switching (Rear Side).
172 HEGO sensor circuit indicates lean. (Rear Side).
173 HEGO sensor circuit indicates rich. (Rear Side).
174 Check for diluted engine oil.
175 Lack of HEGO switching (Front Side).
176 HEGO sensor circuit indicates lean. (Front Side).
177 HEGO sensor circuit indicates rich. (Front Side).
178 Check for diluted engine oil.
179 Fuel system at part throttle lean adaptive limit, system rich (Rear Side).
181 Fuel system at part throttle rich adaptive limit, system lean (Rear Side).
182 Fuel system at idle lean adaptive limit, system rich (Rear Side).
183 Fuel system at idle rich adaptive limit, system lean (Rear Side).
184 MAF sensor input voltage is greater than expected, in range.
185 MAF sensor input voltage is less than expected, in range.
186 Closed loop injector pulse width longer than expected.
187 Closed loop injector pulse width shorter than expected.
188 Fuel system at part throttle lean adaptive limit, system rich (Front Side).
189 Fuel system at part throttle rich adaptive limit, system lean (Front Side).
193 Flexible Fuel sensor circuit failure.
211 PIP circuit failure.
212 Loss of tachometer/IDM input.
213 EEC SPOUT circuit open.
214 CID circuit failure.
215 PCM detected coil 1 primary circuit failure.
216 PCM detected coil 2 primary circuit failure.
217 PCM detected coil 3 primary circuit failure.
218 Loss of ignition diagnostic monitor signal-left side.
219 Spark timing defaulted to 10 degrees, spark output circuit open.
221 Spark timing error.
222 Loss of ignition diagnostic monitor signal-right side.
223 Loss of dual plug inhibit control.
224 PCM detected coil 1, 2, 3 or 4 primary circuit failure.
225 Knock not sensed during dynamic response test KOER.
226 Ignition diagnostic monitor signal not received.
232 PCM detected coil 1, 2, 3 or 4 primary circuit failure.
238 PCM detected coil 4 primary circuit failure.
241 Ignition control module to PCM ignition diagnostic monitor pulse width transmission error.
244 Cylinder Identification circuit fault present when cylinder balance test requested.
311 Secondary air injection system inoperative during KOER self-test (bank #1).
312 Secondary air injection system misdirected during KOER self-test.
313 Secondary air injection system not bypassed during KOER self-test.
314 Secondary air injection system inoperative during KOER self-test (bank #2)
326 PFE sensor circuit voltage lower than expected.
327 PFE sensor circuit voltage below Self-Test minimum.
328 Exhaust gas recirculation valve position sensor closed voltage lower than expected.
332 Insufficient EGR flow.
334 Exhaust gas recirculation valve position sensor closed voltage higher than expected.
335 PFE sensor circuit voltage out of Self-Test range.
336 PFE sensor circuit voltage higher than expected.
337 PFE sensor circuit voltage above Self-Test maximum.
338 Engine coolant temperature lower than expected (thermostat test).
339 Engine coolant temperature higher than expected (thermostat test).
341 Octane adjust service pin open.
381 Frequent A/C clutch cycling.
411 Cannot control RPM during KOER low RPM check.
412 Cannot control RPM during KOER high RPM check.
415 Idle Air Control system at maximum adaptive lower limit.
416 Idle Air Control system at upper adaptive learning limit.
452 Insufficient input from VSS.
453 Servo leaking down.
454 Servo leaking.
455 Insufficient RPM increase.
456 Insufficient RPM decrease.
457 Speed control command switch(s) circuit not functioning.
458 Speed control command switch(s) stuck/circuit grounded.
459 Speed control ground circuit open.

mileage on motor?..overheating history?