I think it should in my opinion, it seems like a much more accurate title for the category

The wiki page says Sexy Hiking was made in 2002. The version that is on Jazzuo's website might be more recent and made in 2004 (because there are different blocks) but I think the first version was released in 2002. https://imgur.com/a/tPvF5

Edit: Since this is the wiki page of Getting Over It, it's possible they just took the date from the game, and it's also possible that Bennett Foddy was wrong about it. It's really difficult to find the actual date the game was published.

Another Edit: https://imgur.com/a/0q7lf I downloaded Sexy Hiking from gamemakergames and checked the properties, and it turns out it was modified before 2004.

Does this count as a skip? https://imgur.com/a/SyE0t

Since the rules mention "Time will begin upon completion of the loading period after pressing "Start"." Would it be okay to save a game and load it at the spot he spawns at? If so, are there any downsides to this?

So apparently, this works

I could imagine this could take only 2 seconds when optimal, plus, if warping too far down is a possibility, as with all of the other warps, you could potentially instantly warp to the end. Sometimes, this method flings you down, and that seems to be the fastest way possible, and other times, your head gets stuck in the ceiling, like in my clip. (slower but still quick)

(Edit: I found a setup that makes this more consistent, line the hammer up directly above the center of his head right as you start moving, and when you are about to reach the very left, pull down and ever so slightly to the right, and it should clip through)

I managed to get a different warp on accident, but it is sorta inconsistent. Here's a video of me doing it pretty quickly (run starts at 0:23)

As far as I can tell, you want to line the hammer up directly above his eye and go straight down (maybe a bit to the left) quickly.

(edit: after doing it for about 10 more minutes, I can get it around 6/10 of my attempts, and it's not even that inconsistent.)