The A/C clutch is probably going bad. I'd just replace the compressor, orifice tube and accumulator, vac out the system and refill.
I don't see why your trans would be bad if the engine has a spun bearing. Not related. Are you seeing increased RPM's when pulling up a hill indicating slippage? How's the trans fluid look/smell? Wipe it on a white towel and note the color. Should be nice and red.
Oh, and don't mix green coolant with the orange dexcool that is stock on these cars. They will do exactly what you see now (sludge). This is also an indication that the coolant is old and needs to be flushed. This could clog up the heater core and radiator causing cooling issues with the new motor.
