1999 Dodge Intrepid Intrepid is Possessed

Sounds like a PCM problem, check PCM grounds, If OK it may need a trip to Chrysler to do a reflash!

Just so you know, 2.7 and 3.5 engenes may run on the same PCM, but they have different calibrations and different parameters, PCM reflashing is COMMON to fix drivability issues, even on cars that have NOT had engine swaps! If MIL is on, have the codes read with a scantool, Autozone does it free. PCM Controls more on Chryslers than on other makes. Charging system for one! One problem that does come to mind is it sounds like it happens when the PCM goes from closed loop(cold operation) to open loop(warm operation) This is when the 02 sensors come online, if you swapped engines because of a blown head gasket, it may have a bad 02 sensor or two, here's why:
All types of O2 sensors can also be contaminated by silicone from coolant leaks inside the engine (blown head gasket or cracked head), and by phosphorus from burning oil (worn valve guides, rings & cylinders).
If you suspect an O2 sensor problem, the first thing you should do is check for any codes that would implicate the sensor circuit. A code by itself doesn't necessarily mean the O2 sensor is bad, however. It might be a wiring problem or something else. So always check the operation of the sensor to see if is is functioning properly before you replace it. If there are no codes, that doesn't necessarily mean the O2 sensor is okay. In many instances, a sluggish O2 sensor may not be bad enough to set a fault code but will still cause an emissions or drivability problem. According to one California study, 70% of all fuel-injectedvehicles that failed the state's emissions test failed because they had bad O2 sensors. Yet few of these vehicles had check engine lights or fault codes that indicated a faulty O2 sensor.