There are a couple of Audio Research Integrated Amp options you may want to consider. Both are above your budget off the shelf new. but sell in the 4500.00 to 5000.00 range used.
I have not heard either of these integrated amps, but based on other AR equipment I have heard and reviews of both these I/amp's, I would be incline to find a nearby dealer and have a listen
http://www.stevehuffphoto.com/the-audio-research-vsi-75-integrated-amplifier-review/
https://www.audiogon.com/listings/lis952d5-audio-research-vt-80-1-year-old-tube
I have not heard either of these integrated amps, but based on other AR equipment I have heard and reviews of both these I/amp's, I would be incline to find a nearby dealer and have a listen
http://www.stevehuffphoto.com/the-audio-research-vsi-75-integrated-amplifier-review/
https://www.audiogon.com/listings/lis952d5-audio-research-vt-80-1-year-old-tube