here's a thought. there are capacitors which can alter the frequency response, or at least alter the tonal balance, perhaps emphazing the lower frequencies and reducing the presence of treble frequencies.
replacing caps in the signal path with mundorf gold/oil or audio note copper/oil
after selecting a "decent solid state amp", even if that solid state amp is not "tube like" in the classic sense may solve your problem.
you may be able to get by with an odyssey khartago, from Klaus, at about $800 and replace caps.
as has been said, a solid state amp probably won't sound like most tube amps.
considering that i am a current owner of two tube amps, looking for a solid state amp, my criterion for a ss amp is one which is well balanced, and reasonably full-bodied, without having to sound like a tube amp in a blind test.
you might want to look at the latest issue of the absolute sound. there are a few inexpensive amps recommended. try to listen to them, or pick one and consider cap replacement. yes, i know, reviews are what they are, but if you replace some key parts you may be able to alter the sound resulting in an acceptable amp.