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

+1 Douglas

Have you recapped your preamp recently?

I am frankly puzzled by your approach. I don't think a more powerful amplifier is the solution.

Shadorne:
Thank you for your input.  A more powerful amp may not be the solution.
Recapping the preamp is probably a good idea. It’s one of the things I was considering. 

Shadorne:
Thank you for your input.  A more powerful amp may not be the solution.
Recapping the preamp is probably a good idea. It’s one of the things I was considering. 

I’m beginning to think I need about 200W per channel, as my 160W monoblocks are not quite doing the job.
Maybe the way to go is solid state at the price range I’m looking at ($2000-3000).
Any opinions on which way to go?

Well, if 160 watts is not quite getting the job done, 200 watts won't give you much more, maybe 1 dB if you're lucky.
I would think you would need 300-400 watts to drive those speakers.

300-400 watts, for $2-3K, yeah, you're only choice is solid state.

Or, as Douglas and Shardone have implied, get different speakers which are easier to drive.

Easy squeezy. Try an Inspire amp by the famed Dennis Had - They're less than $2k. There are tons of tube amps below $3k, primaluna among them.