Is it possible to buy a decent tube amplifier in the $2000-3000 range?

+1  Change the speakers.

Music Reference RM-200 Mk.2. Occasionally available used for around $3000. Or an RM-9 Mk.2, for around $2000. The RM-200 is a tube amp unusually good for use with low impedance speakers, due to it's lower-than-normal output impedance and increasing power with descending speaker impedance.

With barely "efficient" speakers (allegedly 91db) my $1200 (1500 new when available) Dennis Had Fire Bottle SEP HO amp, designed and hand built by a genuine American geezer (only mentioned because hand wired SE amps from some places cost multiples of this…Shindo anybody?), is one of the best sounding amps I’ve ever heard and produces some genuine loudness with its mighty 12 watts per side (or 17 watts…not certain)…a world class amp which made me reconsider my opinions regarding wattage and geezers.

I also recommend Primaluna. You can frequently find used product online. I would look for the dialogue series over prologue. I think echo audio in Portland had a great deal on some mono blocks. You could buy one and use in stereo or buy both. They do sell online but don’t always ship depending on the product. I have a dialogue one integrated and I love it. 

I'm running a Conrad Johnson Premier 11A and with the right tubes I am very happy with it!