I didn't check alot of the details you did when my RCM went out, but it certainly does sound similar. If you're familiar with soldering, you can fix the whole issue in less than 5 minutes. I think a new one is $170 bucks. If you pull the RCM out of the black box on the passenger side of the engine compartment, undue the fuses and unhook the cables, the module will come right out. Take a look with a jewlers lens or soldering magnifying glass and see if you see any small cracks in the solder on your circuit board. If you see one, you can test it with a voltometer (which I did) to determine if you're worried it is the correct spot or not. Typically the reason the car is so tempermental when faced with this issue is because the solder will get hot and seperate then when it cools back down it will mesh back up and work again. You can tell the board is laid out by a machine due to the size of the solder joint (very small). But a dab of solder on it, retest w/ voltometer, put it back in and no more problems. I also discovered the spuracity of the RCM was the root cause of an frequently reoccuring Check Engine light which has since not came back on.