Just to add my two cents about the humming sound, here is my story. I am not asking for any help/advice (yet), but maybe what is happening to me can help racecar somehow:

2005 Roadster acquired 3 months ago, 80000 miles, everyday drive. I have noticed the EXACT same humming sound as described by racecar.
- only starts when turning the key to ON position.
- keeps going after the engine is started and running
- keeps going when driving.
- will go away after driving for about 5 minutes.
- no such sound for the rest of the day once the car has been driven at least once. In other words, sound present when starting and driving the car for the first time in the morning on the way to my work, no sound in the evening even though the car has been sitting on the parking lot for 8+ hours. Have yet to confirm if I have the sound EVERY morning. All I can tell for the moment is it happens often, but have not paid enough attention to guarantee it is there each single morning.

The sound is not the AC fan, and it definitely feels like it is coming from behind the dashboard. Before I knew anything about the Xfire, I thought it was the hydraulic pump for the top getting some pressure in the cylinders, only to realize later on that this pump was located in the trunk and only operates when the top is operated, so that cannot be it.
Now get this: last week, I got the whole "no unlocking with FOB + alarm turns ON when opening the door manually + no start issue on the parking lot". Old posts on this forum saved my *** as I just had to disconnect the - terminal of the battery, wait a minute, and voila, FOB disengaged the alarm and car could be started. Have not investigated the issue yet, could be many things (CLP/SSM, SKREEM, car battery etc.). Also, my alarm (the sounding part at least) never worked since I bought the car. I know for sure as I have triggered it in the past and all it does is the lights are blinking and I hear a relay click somewhere. I also do not have the lock/unlock chirp, but my understanding is this is normal if I do not have whatever newer module installed instead of the original.

So, what I am saying is I do NOT think the humming sound you hear is your alarm dying. Reason for that is I get this sound while unlocking the car normally and driving it. I would not if the alarm was trying to sound.
Does that mean the humming sound is related to a malfunction also related to you issue, I have no idea. I find it odd that we are the only ones who have noticed this sound and we both have similar alarm issues.
It would be interesting to know if other people hear that humming the first minutes the car is running, and if they ever had the alarm issue, at least you could rule out this sound as a reason for what is happening to you.

I will keep an hear on this sound and try to find out where it is coming from ...

Alex