Limited runtime is a thing with my Nikons, ( about 15 or 20 mins ) so i guess it may well be a thing with all DSLRs that also do video. A camcorder would be better in that respect but how long do you need an interrupted video recording to be ?
You only need enough recording time for the length of any track. 3 or 4 minutes, unless you're a prog rock extended songs crew.
If you only need to record regular songs, a DSLR will be fine, as long as you stop the recording after each song. The limit then is just the card storage. Get a big one.
If you can get deals on a Pansonic, i would go down that route.
The lighting would be troublesome for either option, depending how bad it is. You may need to up the ISO but as you know, high ISO introduces digital noise.
Experiment first