93 Lincoln Conti. Runs rough in gear

Have you cleaned the throttle body bore and plate of carbon/deposits ? This can cause idle and off idle symptoms .

back firing through the carby is an indication of valve timing, bad valves, ignition timing or crossed HT leads. Check the firing order

engine mounts are bad

Do you know what engine scan data is ? Disconnecting sensors is not the way to find a problem ! What is the computer seeing as data input signals . Is the vehicle in closed loop fuel control , is the EGR opening when it shouldn't be , Is the PCM controlling the idle air control valve or is the vehicle drive by wire (electronic throttle control ?
005 Idle Speed Problems Idle Air Control Test
007 Idle Speed Problems Scan Data for Idle

new carbie???

It may have a vacuum leak, and /or a dirty carburator that may need to be overhauled.

probable vacuum leak query brake booster

If it does not do it in park or neutral, it could be a number of things. One being a sticking Torque Converter Clutch solenoid (TCC). It could be that it needs a simple tune-up. How often does this problem happen?

has it had a tune up?

put a throttle position sensor on the throttle boby this should fix the problem!