I don't know the answer to "Can I get the set tube sound with solid state ?". But let me respond, anyway.
Your room is a bit smaller than mine - mine is 13x24. I have the Super Eclipse with Welborne Lab Laurels. These are 300B based SET - output of 8w. I've had mine for 8 years or so and there have been no issues, and tube life is far greater than I had imagined. I think your speakers are just slightly more efficient than mine.
You say you don't have the money for tubes, but you do have $2500 to spend. You could look for something like the Welborne amps (the Laurels or the later DRD model) used - probably about a grand.