Horrible resonant frequencies at certain frets

I do not hear a resonance can you provide more info on the time where it occurs, you are playing many notes. You have to ask yourself what could resonate on a solid body electric? This is typically something that happens on an acoustic.

What I hear is a possible fret buzz, and based on the wave file it isn't that bad.

If tweaking the bridge didn't help you may need to adjust the truss rod. When you put new strings on where they a different gauge that the previous set? This will change the stress in the neck causing it to bow. Also, over time frets do get worn down. Is it possible that some of the frets are slightly lower than other? This is a typical cause of buzzing and dead notes. All of this depends on how long you've had the guitar and how much playing you do.

My only advise would be find another luthier and try it again. The last guy might have missed something. I assume you are playing the same way before and after this happened right? It might sound like a stupid question but the fact is that you can make any guitar buzz by attacking it too hard. I once had a tech set up my guitar with the action so low that it would buzz if I plucked with any amount of force I deemed normal. His opinion was that, as a shredded, you should barely pick anyway and that the set up was ideal. That was based on his opinion. I play with a little bit of a punch and I told him that I didn't mind if the ax "bit back", indicating that I don't mind a slightly higher action if that means I get NO buzz. He gleefully complied with my request at no extra charge. The point is that your music shop guy might have done some other adjustment that is not conducive to your playing style.

If the guitar was ever in better shape there has got to be a way to get it back to that state. Sorry I couldn't help more but these things can get tricky and without holding it myself I can only guess.

There is a couple of things I would check. The first is, does this still happen when the other strings are muted? And the other thing is are the new strings the same brand, gauge, and kind/style as the old strings were? I have found that sometimes one string being played can cause sympathetic vibrations in other strings if they are not muted and I wonder if this is happening in this instance. Also, I would look for a luthier who knows what the problem is and can make adjustments needed. All luthiers are not created equally skilled.