@erikt
I’ll try not to come off as a fanboy (I’m not actually, just a satisfied user) for Audio Note but your speakers are the real pearl in your system. The Super K’s are wired internally with $1,000 per meter cable and the crossovers are populated with top shelf parts. The resolution and transparency of which they are capable will surprise you. That’s why earlier in the thread I mentioned that you really haven’t heard what they are capable of. The Super K’s are perhaps $15k retail IIRC.
To piggyback on some earlier suggestions, the two integrateds that really stand out (that I have heard with these speakers) are the Leben cs300xs and the Audio Note OTO SE Signature. The Leben has more power and dynamic snap while also delivering lovely tone, texture and resolution. Its a push-pull design and deliver maybe 15wpc, so it does not meet the single ended (pentode) criteria you shared in a recent post. The Leben does perhaps give the false sense that it has more power in reserve than it actually does because so much of the potential volume comes on quite early on the volume pot. Responds very well to tube rolling and sounds great right out of the box with stock tubes. Hard to go wrong with this choice and it can be found preowned in/under your stated price range. An added bonus is it has a nice bass boost (the 1st click is nice, the second click-not so much) function. Robustly constructed like the heirloom piece that it is. A timeless amplifier that can be end game, depending on your sonic goals. The only downside is you really should utilize Switchcraft terminated interconnects.
The OTO SE Signature would come in above your stated budget of $4,000 preowned, so I won’t spend alot of time describing the sonic differences between the two other than to say it is better musically in every objective criteria than the Leben EXCEPT dynamically/power output. It is a paralell, single ended pentode design so you get a large helping of the SET flavor you mentioned earlier. It too can be an end game amplifier with the K’s if you can swing the additional $$$ and live with 10wpc vs 15wpc. The Leben responds more positively to tube rolling than the OTO...for instance, drop in a quad of NOS Mullard el84’s and a pair of NOS Mullard 12ax7’s and the Leben transforms....the OTO with that same set of tubes will sound flatter and somewhat lifeless. Circuit design differences (the OTO SE Signature has a true preamp stage, the Leben is passive with just switching and volume) I guess...neither is more right or wrong, just different.
Some arbitrary guesses...with your Luxman, you probably rarely leave its class A bias output to slide in to class A/B...so you are probably hearing (arbitrary guesses for comparison’s sake) 70% of what the Super K’s are capable of. With the Leben, you would probably hear 75% of their capability, with the OTO SE Signature, perhaps 80%. Add in a full set of complimentary (to your ears) Audio Note interconnects and speaker cables...perhaps you could reach 85%. To hit 90% and on up would likely require source upgrades and then next level Audio Note amplification.
Good luck with your next steps...its an itch worth scratching and you will always wonder if you dont. Its not for everyone but there are an awful lot of music lovers and musicians who wind up with Audio Note systems...however, the Leben will be easier to track down and carries with it alot of opportunity to explore the tube side of the hobby.