I haven't checked out ^^^that clip yet, but I'm betting one of those "unexpected and awesome" cover songs is Madonna's "Live To Tell" right? I heard his trio with Joey & Kermit play that at The Knitting Factory (original location) sometime in the early 90s and it nearly brought me to tears.
The youtube "You Probably Like This..." algorithm has pretty much figured out that I'm a sucker for anything featuring Bill Frisell, or Pat Metheny, or John McLaughlin, or Allan Holdsworth, or Herbie Hancock, or Chick Corea, or Lee Ritenour, or Simon Phillips, or Snarky Puppy, or Dave Weckl, or Wes Montgomery, or Dennis Chambers, or Frank Zappa (okay, most of those Zappa clips aren't "jazz") so that's what I've been listening to lately.