You can use solid state to make a TEA Laser psu, but not a commercial one. Commercial ones have to be GFCI protected and the EMI from a spark will trigger the GFCI and shut down the psu.
I have a supplier for cheap and reliable NSTs if you need still. He's a colleague of mine who is RIT's summa cum laude in engineering and physics. I can put you in touch if you like.
The dielectric and rail electrodes are key, an error or inefficacy in either will cause failure to lase. Overhead transparencies work best, but other alternatives exist. The trick is a thin dielectric for minimal inductance. You need a super fast rise time to produce the pulses needed to get lasing.
Alternatively to the NST; you can use a cheap flyback and driver with good results. A simple 555 driven IRFP260 in single ended operation can achieve the voltages needed easily. The trick is to put a higher than normal primary turns ratio in order to lower the step up voltage. 12v supply through about 25T should do nicely for an average flyback.