Recommend me a Class A Integrated Amp (or sound like Class A amp)

How about the Sugden A21 or A21se? The A21se was $3250, could be a bit higher thanks to inflation. 30 watts pure class A 8 ohms, 40 into 4 ohms. A wonderful amp with great reviews everywhere....sounds way more powerful than those specs suggest. You would save lots of money, yet have more actual power in class A.

You've already captured the basic trade-ofs of class-A: the lowest distortion at the cost o vastly higher heat and consequently lower power (since ne needs to get rid of that heat).

Note that there is no fundamental difference between a class-A and a class AB amp.  you can take any of my designs turn a potentiometer and voila, go from hgih bias class AB to class A. It will then gradually either burst into flames or blow the fuse (it will do the latter).

A good AB design will in fact be class A for small signals.  All "nuance" and "detail" is, by definition, a small signal. So those are class-A anyway in a design like mine, and i am far from alone.  So i would suggest that you look for a well designed, high biased AB design as well. I suspect they are indistinguishable from pure classA except by using a thermometer, fire extinguisher, or if you need a bunch of power and headroom ,when the AB will be superior, since the designer can make it more powerful.

I wish i could say "buy mine" but with pandemic shipping and supply chain problems its sitting in pre-production land.

Oh, and "dont fix what aint broke" it sounds like you are very happy. Is there not a better place to therefore put your money? DAC? Turntable?  Beaucastel Homage '89?

Those who I have spoken to echoed the few comments earlier that I would probably see marginal improvement upgrading my amp since my Sony amp is considered as a superb amp almost comparable to the higher end Japanese brands. 

So I might decide to upgrade my DAC or speaker first. 

I did not see anyone mention any tubed amps. I purchased a Rogers High Fidelity EHF 200 Mark II integrated direct from Rogers that was a trade in to him for his really big amp for right about your price range. Full Lifetime warranty!100+ all class A watts / channel !  It’s big, heavy, very well built w/ all point to point Teflon coated silver plated wiring & most importantly, sounds excellent! Very powerful, dynamic with the subtlety & nuance that very few but the best solid state amps can match. 
 

For myself, once I heard what a good tubed amp can sound like with good speakers in a good system, there was no going back to solid state. Sounds so much more like live music w/ “air” & space around each instrument or voice & not fatiguing at all. That all does come with a price of initial expense, tube replacement expenses & heat but I think worth it. 

The coming of a big, powerful amp ( 2-KT 150’s on each channel & classA operation means it foes  put out plenty of heat so it needs to be well ventilated & not in a small room in Florida w/ no AC! 
 

ime plinius are on the darker side of neutral, as are the top ayres (less so than plinius, but still...)

krells, mccormacks (smc modded ones) have more extended airy treble but can be a little revealing on less well recorded material

most pass labs amps and accuphase have quite extended treble but add some warmth to the midband and midbass

top hegels, classe, belles class a, exposure, and certain first watts are most balanced in sound, not lean not rich not bright not dark

devialet and agd are a somewhat different breed, saturated yet very extended, ultra smooth, devialet a bit more colorful and forward, agd is fast rich silky smooth