Fazer pianos from Finland used plywood soundboards. I am not sure, but at least 40 years back. Terrible sound but I do not think they would have been better with a normal soundboard.On the other hand the old pianos with metal soundboards, fooled many pianists. Many found these pianos quite okay as long as they did not know about the soundboard.The same thing happened when the first plastic actions hit the market. People liked the pianos, untill they were told about the plastic. They were made in Sweden.I think Steingraeber, and maybe others, are making experiments with soundboards made of carbonfiber with a layer of spruce on top.Maybe the Yamaha pianos with plywood sounds great? I have never seen them.
I'm a fan of Baldwin Hamiltons myself. A real workhorse with good projection. Nothing fancy, just a good solid instrument. I have a Charles R. Walter that is well constructed, good tone and a solid bass for a 44"er. Falls in the ballpark of your budget with some negotiating. Lists for roughly 10K.What size piano are you looking for and does it have to be new?
I've heard kawaii is only a mediocre piano from some of my friends. Maybe you should avoid specific Kawaii pianos. I don't know which pianos though.
Plywood doesn't have to be junk. For the historically minded, may I bring to your memory that one of the best -- if not the best -- overall airplane of World War II was the de Havilland Mosquito, which was made of ... "plywood".
My main issue with uprights is the action: many are too heavy, do try your selections out and see that the lightest leggiero prestissimo is feasible.