I haven't checked a schematic to be absolutely certain, but I was told that the FT-60R will automatically limit charging of the battery once it is full. I took the AC adapter and used the cable to connect it directly to my 12v power supply (and just leave it connected) and have had no charging issues and have the same performance since the day I bought it 7 years ago.
Wow! 7 years sounds like a sufficient battery test to me! I'll charge it overnight next time and see what the voltage shows then at power on. Sounds like I don't have anything to worry about though. I knew there were a lot of these units out there and someone here would have long term experience with one.
Thanks again to all!