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

There is a Primaluna Dialogue Premium Integrated in the classifieds right now for $2700.  That would be a great tube preamp for you to consider.    

+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.