I'm not sure if I'd like Meat to sing Always or Bed of Roses. I love both of them, but they're Bon Jovi's songs. They're to him as Bat or Anything for Love is to Meat. Anyone else covering them just wouldn't be right :P
This Ain't a Love Song, on the other hand, I could see working
I reckon Meat could do a pretty cool Meeting Across the River. Justin on the piano and Dave on the sax (for the trumpet part). It could work
Or how about Michael Bolton's I Can Go the Distance?
OR...Boomtown Rats' I Don't Like Mondays?