Looking for a SS integrated Amplifier recommendation going into a new system

I have similar musical tastes to yourself and home demoed a few SS integrated amps. It is worth trying to hear a few as some, to my ears, are over-detailed and fairly dry sounding compared to the sound signature you describe that you prefer.  I would recommend Vitus for a very natural, slightly warm, very rich sound, especially the SIA-025 which is class A. Or for a warmer, more velvety, but less detailed, sound then the Luxman range. 
Personally I preferred the Vitus as the Luxman sound was a bit too dampened, but on certain music it shone. Given the warmth of a 50s Sinatra recording and the Luxman was to die for. But move to a classical piece and the Vitus shone brighter.  Overall to my ears the Vitus has the best of all with little compromise. 
I have not heard Pass amps but hear good things. 

The musical fidelity mx8i or a second hand Daniel Hertz. But the mf is much bether than the luxman.

Thank you all, again, for all the great inputs.

This is going to be an interesting journey in the next few months to see what works the best in my system.  So far, I am very high on the two class-A integrated amps recommended, the Pass Int 25 and Luxman  590AXII, mainly because I also plan to see how well they will drive my headphone that I listen to quite a bit.  Meanwhile, some other recommendations also got my attention, such as Hegel, Belles...etc., I will see what I can do to get some of these amps for a home audition.

On a separate note, how is Sugden integrated amp offering?  Is it worth to look into further?

The Boulder 866 gets stellar reviews.  Very neutral leaning slightly to the warm side. I have one on order to pair with Rockport Avior ii on order as well. A little above your price range new  so perhaps used. Good luck in your search!