Line Magnetic was mentioned, along with Leben, and Luxman.
The benefit of a $6k budget is a wide selection of available choices.
I would listen to as many amplifiers as possible. I would purchase used equipment, because I know I could resell for my cost (or at a small profit) if needed.
I would start with a Line Magnetic or Triode TRV 845 Class A SET amp. Then move on to EL34 and KT88 amps from the same companies. I have a Triode TRV 845 PSE. Sublime sound, and rock steady reliability since I purchased the amp about 5.5 yrs ago.
Cary CAD 805 (there have been several versions of this classic design over the years). For some this is a benchmark Class A SET amp. Others believe it is not accurate to some degree. Listen and decide for yourself.
In my opinion, Leben is the equivalent of a golden age amplifier that is completely restored using new close tolerance and higher quality parts. A mix of classic and modern sound.
There are several Audio Research and Conrad Johnson amplifiers that sound wonderful and are easily found. I regret selling a CJ MV45 and I have an AR D-70-MKII.
Luxman MQ88 has been praised by everyone that has heard it. I use a pr of MA88 / 75th anniversary mono blocks. So relaxing and incisive to listen to.
You may also investigate vintage amplifiers. Caveat is to be sure that the amp is completely rebuilt, not just restored with a mix of old and new parts. REBUILT. Some believe this may reduce value. I would rather have reliability and great sound.... Some may disagree.
The elephant in the vintage room is McIntosh. Many will immediately recommend the MC275. Good amp, but not their best. If you want better sonics, then spend time with a pr of MC30 or a MC240. The MC225 sounds wonderful, but may not be powerful enough for your needs.
Some would recommend a Marantz 8b, which is an easy default recommendation. But I think the Mac 30/240 sound better.
Eico HF89 is a powerhouse of a KT88 stereo amp with a very wide frequency response.
Fisher SA-1000 / EL34 Integrated amp and probably the best amplifier made by Fisher. This is a "final" amp for a discerning few.
Harman Kardon Citation II. You have probably read about this amp. Everything you have read is true. Tube magic, and SS power. Capable of driving any load and delivers an ultra Wide Bandwidth, dead quiet background, brick house reliability if correctly rebuilt. This amp would cost at least $10k if remade today; and likely more than $10k in the current market.
Lots of choices. Potential for lots of fun. Spend the summer acquiring a few amps, then enjoy the colder months by listening at your leisure while you watch the little cities of tubes glow in the twilight.