You guys will have to excuse me but I'm failing to get the logic of the 'correct' type of wood to be used to play jazz. They're drums, you tune 'em up and play 'em. I think you're head choices are going to make a bigger difference than what type of wood it's made out of. The way you tune, the way you play, all that has more bearing than what the kit is made out of. Besides, after the sound guy gets done miking you up, it'll sound completely different anyway. That vintage sound we all hear on the recordings are just snapshots of where the masters were at the time they made the recording. If you were to go into a club that was crowded or an empty hall, I doubt anyone will be able to notice. Ask people what they hear, they'll say "drums", and whether or not it's 'good' or 'bad'. No one will make the excuse that they don't sound right because they're oak, or that you 'should've gotten a maple kit'. If you're playing is incredible, you could be playing a Sponge Bob toy kit and no one would care, right?
I played the Yamaha Oak Customs in a store once and loved it. I could very well have gotten that kit and used it for everything I do, but the word 'Bubinga' sounded cooler so I went that way. They both sound similar, just more syllables with 'bubinga'. But I've played them all: maple, birch, mystery woods, and now birch/bubinga, and I've never had a problem with making any of them work for whatever I was doing. So what's the big deal? Go get them, use them on a gig and report back. I'm betting you'll love them.