Can you describe what you mean by glitchless? As in, what would be removed from the existing categories.
You play the game the way it was meant to be played. Without using any glitches that gives you an unintended advantage. For example: https://www.speedrun.com/tr2013#Any_no_DLCs - Here's a subcategory glitchless.
It's kind of hard to define how the game is "meant to be played". For instance, there is a way to get out of bounds in P2C3 without the use of glitches (although we usually use the superjump, just because it's faster) and this causes a complete sequence break that skips about 60% of the level. At this point, we would have to very specifically define what is allowed and what isn't, since you can technically play the game without using glitches but not the "intended" way.