Try changing the temperature sending unit. This regulates the cold start mode and it appears it's still in cold start mode and still feeding it too much fuel, causing a flooding condition and making it die at stops. When you depress throttle to go, it's still getting too much fuel and wants to bog and die on take-off.
In that 30 to 40 min. when it won't start , check for spark at the coil ! Pull a plug wire off the engine , an hold near ground , If no spark could be the ignition module . Which engine does your caddy have ? 4.9 or 4.6 L