Looking for new speakers

See my Tekton Moab thread. You don't have enough budget to do any better without going to Encore or Ulfberht. Which you are welcome to do. Double Impacts will be better in every way than your Thiels. 
Moabs are considerably better than Double Impacts. The other two are better still, but Moabs are the killer value.  

Your premise however is iffy at best. There's genuine audiophile demo tracks recorded with electronics made from before Mr Thiel was a gleam in his daddy's eye. So that ain't it. What it may well be however is you're listening to reissues and assuming they're the best because that's what the ad copy says. With records however no such luck. Quality varies tremendously from pressing to pressing. Two identical copies never really sound identical. Quite a lot of them are not all that good. 

Your records will sound better than ever with any of the Tektons from DI on up. The same distortion you are hearing will still be there. It will be more clear, but not more distracting. A strange thing about incredible detail, it makes the music so much more clear its distinct from the noise and so the noise actually bothers you less. May not sound logical but the same thing happens with the best cartridges, the music is much more clear and the surface noise seems to disappear. You will get this with better speakers. Excuse me. Tektons. Don't hold me to that if you decide on something else.

Millercarbon: how much does Tekton pay you?  If nothing, how boring is your life that all you can do is literally push Tekton speakers at every opportunity you can?  

If you hear distortion with new gear upstream, can’t rule out the possibility something there is the source. If it corresponds to the speed of the turntable, could well be an issue with the phono section of your system.

What cartridge is being used? Moving coil or Moving magnet? Is it properly connected for that to the amp? Is it possible the stylus on the cart is damaged or worn? Do you hear distortion with non-phono sources?

Just some things to consider before assuming it is the speakers. Many ways to produce distortion if a phono rig is not set up properly.

FWIW those Thiel are as good or better than most assuming they too are in good operating condition.  Damaged crossover tweeter or other drivers would likely cause distortion.

If the distortion is associated with higher volumes with any source could be amp clipping. THiels are not efficient and usually require a lot of power and current to sing. but that Luxman should be up to the task.