When you say you noticed the voltage dropping slowly to 11V, did you see that on the Silverleaf as an alarm condition.
I ask because when my alternator went bad the second time after having been rebuilt less than a couple months prior, the Silverleaf popped up the indicator of battery voltage and it was showing around 12.3 or so, and it proceeded to decrease. When we stopped for dinner, I switched off the C12, but wanted to run the generator to help fix dinner in the microwave and it wouldn't start (turnover), and neither would the C12. I tied in the house batteries and got the generator running, then we fixed dinner and by that time the C12 would again start with the generator running. I left the generator on. Our alternator had burnt up once again, and the shop determined that for some reason the alternator remained at hi output (over 15V) and they couldn't determine why since it worked fine on their test bench. Their fix was to limit the output of the alternator to 14.2 no matter what the incoming request was.
As documented on the forum before, something in my system takes a volt away from me by the time the alternator charge hits the batteries so my Silverleaf now reads from 12.7/8 to 13.2 while driving which is my new normal until I finally trust somebody to figure out the issue rather than simply throw time at it. For 2 years now I've gotten away with merely have 13.2 volts charging to the chassis batteries. I keep promising myself to check the ground connection on the chassis. Where is that anyway?
Mike