If you are going for a vintage amp I would just make sure that it has been well-restored. Capacitors wear out and, though a older unit may work well initially, if it is untouched you may be looking at an eventual repair. That said, the combination you suggest could be very nice indeed. I had a Scott, I think it was a 296 version, that was restored by the late George Wright, that sounded very nice with Heresys, among others speakers I tried it with. Eico would also be another good bet. Stereophile renewed the popularity of that companies HF-81 with this review. There's also plenty of good affordable contemporary tube amps that would foot the bill. I'm selling a Sophia SET Baby that would be great with Klipsch, but it is limited to only a single pair of inputs so would not work unless you added a pre. Quicksilver's amps work great with Klipsch, but also would require a pre. The usual suspects of the latest amps from the far east would also probably be a nice option (Cayin, Mystere, Prima Luna, etc.). With your turntable you will need a good phono stage though. I'm not sure how the phono stage is in those integrated amps from the past. My friend used to have a modified Dynaco that sounded very nice, but he was using an Audible Illusions pre with it. If you have the space, I'd go for the fuller range of the Cornwalls over the Heresy, though you didn't say how small your room is, so that'd be a tough call as the Cornwalls are pretty large. Another good option would be the latter-produced Forte II's, which can frequently be found for $500-600 or less if you get lucky. I found bass to be lacking in the Heresys but otherwise they were very nice. You can find more info on HH Scott amps here, and of course the The Klipsch Forums are a great resource for Klipsch.
Good luck - it's a very nice direction to go in for Jazz. Tubes and horn speakers are very nice together.
Good luck - it's a very nice direction to go in for Jazz. Tubes and horn speakers are very nice together.