Maybe stupid but maybe worth a try.. have you tried pulling out the empeg just a little bit of the docking sled (so that the connector isn't connected anymore).

But later that night, holding the new remote over the hood didn't do anything until I opened the door and pulled the empeg.

Can you lock/unlock you car with the remote while sitting in the car? You could try if it really has something to do with the empeg quite easy this way...

I did that once. I was specificially showing someone how the empeg was preventing the doors to lock, and it locked. I had to pull the empeg out to unlock and disarm the security system. That was the only time out of probably 200 presses of the lock button that it locked with the empeg either playing or in standby.

If you find out that it has something to do with the empeg maybe some cabling is wrong.

I really have no clue what to check on this. I'll have to probably pay an installer sometime to check it out again.