Looking for new speakers

As your Luxman integrated has pre outs and main ins I would look at the Vandersteen Quatro CT. Same first order crossover concept as your Thiels with the addition of the built in subwoofers. But first as tomcic said check with the people on the Theil thread and see if yours just need some TLC. 

If you're having distortion listening to records it's most likely your turntable setup if there a professional near you who can check it out?

1. ignore first respondee.
2. as others have suggested, address audible distortion issue first.  If the Thiels and everything else are performing to spec, you shouldn't hear this.  Try and isolate it by swopping/swopping over components.
3. There are lots of 10-15K speaker threads on here already.  There's a LOT of product out there.  You can run the gamut from Harbeth to Wilson.  

I really don't think there's a problem with the turntable setup -- the dealer set it up in January when I bought it, and I basically have not touched it. The cartridge is a Koetsu black moving coil. It's so new I doubt it needs replacing or tweaking. However I can ask the dealer if he'd be ok with checking out the setup (I am not a person who enjoys fiddling with devices!).

The reason I think it's the speakers, or something beyond the amplifier, is (1) both devices going into the speakers are almost new and of excellent quality and (2) the distortion increases with the excellence of the recording, i.e., Analogue Productions 45s or the like. You can just hear that there's MUCH more information coming through. You can hear that it would sound absolutely fantastic if that information could come through distortion-free. And something can't handle it. Now, there's the possibility that it's the speaker cable, which is the only thing remaining from my ancient old system (the CS3.6s, purchased from eBay, were an upgrade from Thiel 2.2s purchased in 1992!). I plan to try new speaker cables first, but I seriously doubt that's the problem.

I'll see what information I can find out about having the Thiels checked out, and I'll take a look at some of the speaker threads on this site. Thanks for your input!

Agree with others you likely have a problem somewhere.  If you still have your old amp or can borrow one I’d definitely try that to rule out the Luxman as even new gear can have issues, and it sounds like you didn’t have this distortion problem until you started using the new amp or turntable — no?  Also, blown speaker driver or crossover component — is the distortion from both speakers?  If it is, I think it points further to a possible upstream problem.  A bad cable or dirty connection somewhere could also be the culprit, so I’d try cleaning all your connections, which is a good thing to do anyway if you haven’t lately.  I assume you’ve cleaned your records and stylus, but sounds like a dirty needle kinda sound you’re describing.  You’ve got some great speakers, so if you still like their overall sound it’s worth a little frustrating troubleshooting.

That said, as an owner of speakers from a manufacturer no longer in business I could make a case to sell them before parts become an issue — no fun sitting on eggshells wondering when a speaker component might fail.  Plus, it’s not exactly an unenjoyable chore to go out and listen to some new speaks even if you don’t end up buying.  Toward that end and given you’re coming from Thiels, I’d recommend listening to Vandy Quatro, Joseph Audio Perspective 2, and Usher BE-10 if at all possible.  Hope this helps, and best of luck.