I have a PAL PS2 and recently burned a "backup" of an NTSC-J game to play on it. It worked after doing the swap-trick but once the game loaded the screen was skewed upwards out of view and the game felt laggy like it was running at 50hz/FPS and not the native 60 the game is encoded for? Does anybody know why? 

Also if I were to do the opposite and play a PAL game in an NTSC console would I be able to "upscale" to 60? I ask because one of my speedgames (CTR) has free time-saves exclusive to that region but falls short due to lower FPS.

If the above method is viable then which version of the game would I submit to a leaderboard?

If anybody can help answer any of my questions I'd be grateful!

That’s probably a question best asked to try CTR runners as they probably have more knowledge on it. My experience with swap magic is strictly NTSC-U -> NTSC-J so I don’t know for sure how PAL consoles behave with NTSC games although I’d imagine that the console is what is causing the 50Hz rather than an issue with the game. But that’s only a guess.

You'll need to either get your ps2 modded with a chip, 
or use the swapmagic method to get out-of-region games to play.

A PAL PS2 doesn't handle a ntsc any different than a ntsc PS2 would,
the console is region locked for no reason.

Although, since you're using a burned disc instead of the original, 
you could look into homebrew, and use the mode selector to manually switch to ntsc output, or pal60 if your capture card doesn't support ntsc.