Modern Class A SS Integrated Amplifiers

The Luxman L-550AX meets your criteria, its 20wpc pure class A in 8 ohm, 40wpc into 4 ohm, balanced inputs, impressive phono input, and remote control

many favorable reviews about it on TAS/etc, and the power is more authoritative than you would think at the specs.

extremely musical japanese class A at its best

can be had 2500-2800usd used on ebay and 3300-3600usd new on ebay shipped from japan or domestic.

+1 on the Sugden, as well as a +1 for Arizona Hi Fi.

I loved my Pass INT-30A. I only sold it when I switched from Thiel 2.4s to an all Coincident high-efficiency SET system.  It meets all your requirements.

Try a used Pass Labs INT-150. Upscale Audio has two for sale. (One is my trade-in for a tube amp.)

As above any Luxman *Used only* will meet your price. Rare to find , but There are 2 right now at listed at US audio Mart For great price. Excellent stuff. If you want new, Power Modules Belles Soloist 1 is $2900 masquerading as a $5000 INT. Amp. 100 at 8ohms/150 at 4ohms. Very stable, Black background, wide S/N ratio and channel separation. And 2000 damping factor if that means anything to you. I have owned both after too many others auditioned. NO BETTER bang for the buck than Luxman used or a  new Belles.