Thanks for playing!
And you are right: the culprit of the lagging is shader compilation. Indeed, one trick is to load all the shader materials that will be used while being rendered by the camera. I haven't tested it yet, but I've heard that you can make your loading screen almost opaque (254 alpha) and run whatever you want behind it to hide things gracefully. I discovered this issue quite late in the game development, and the optimization is not trivial. The best I can do is leave a note on the game page, hoping that players understand and are a bit forgiving of the disruption.
You're not alone in considering the game too hard for newcomers, but I appreciate the time you're willing to spend to attempt it. I just hope that this genre receives more love, and I'll see what I can do in future fighting games that I make.