So why would the Soundlab sound relatively louder in the treble with a solid state amplifier?
It won't.
It will give you more bass (where impedance rises) - so if anemic bass is your problem then a tube will help.
If you want more midrange then a tube amp will unfortunately reduce the output but you may get some more harmonics in the mids (more warmth) - if that is what you need then tubes are a good solution => more bass relative to mids and more warmth overall. (note warmth is related to loudness in a sense so although mids may lose some power they may sound more "rich")
Good luck!