Thanks for the warning, but no way would that create a problem running a 3/8 setup if everything was correctly matched -- especially with .063. I run a 36" 3/8 .050 full comp setup on a very healthy 066 flat top with over 200psi that would run rings around that saw. Do I need to periodically adjust the bar, sure. Am I 'stretching' the chain? No. Do chains really 'stretch'? No. Does eventual wear between the rivets, tie straps and drive links make people think chains stretch? Yes. And that actually takes some time after initial break-in use has set (pre-stretched?) those stress points. It can be accelerated by using crap bar oil and running in dirty conditions which will obviously speed up the wear process, but nothing stretches. It just lengthens. Or..., the bar 'shortens'.
Check the adjuster and the mating between the bar and bar mount for problems or anomalies. Make 100% sure the studs are completely threaded into the case and the bolt shoulders aren't extended to the point of being up against the sprocket cover when everything is snugged up or are working loose just enough for the bar to slip.
What bar are you using? Does it have the correct sprocket cover?
I'm putting my money on a chain adjustment problem, not the chain -- certainly not the mods., But that said, it definitely sounds like you covered quite a bit of territory there to build a very cool saw. Pics and vids are always appreciated!