I'm not very familiar with PS1 emulators but maybe there is one that overlays some text as long as the speed up feature is being used? While it would suck limiting people (who want to use speed up) to emulators that can do this, it would make retiming much easier as you'd just need to count the frames during which the text is shown.

And people who don't use speed up could still just run on their emulator of choice.

As for detecting people abusing it: If someone ran the game at a very mild speed increase (like 1.01x) it would be difficult to spot just by looking at it, but you could try to find a part in the run where they walk for x tiles nonstop and check how long that takes. Although such a minor speed increase wouldn't improve their time by much anyway (and a big speed increase would obviously be noticeable).

I don't see how it makes it unfair if the loading time gets added back or entirely removed from all runs (one of these obviously must be done).

It would definitely increase verification/timing efforts quite a bit, the question is whether it's worth it overall for the community. If the amount of runs using it is small, it's probably okay. I'd even be fine with retiming it myself but of course the problem is always whether a runner can be trusted to do it accurately for their own run.

While it is doubtful that I'll revisit the PS1 version in the first place, I definitely know I won't run it with the default loading times. If it does run faster on other consoles, that might be a fair compromise and the better alternative. I just remember experimenting with some of the emulator settings and not getting any difference in the loading times.

I'd like to suggest to allow the use of a turbo/speedup button while the game is saving/loading. The waiting times when loading a level or saving a character seem to be hardcoded into the game, so speeding those up makes the run much more enjoyable (to me at least).

I did a run almost a year ago (that I didn't submit because I used a 10x speedup during the waits) which you can see here if you're curious what it looks like:

Allowing speedup would make timing runs a little more difficult since you'd have to add the loading times back in order to compare against runs not using this. So you'd have to check/retime every run using speedup. But personally I would not want to run the PS1 version with the slow loads, that just makes it too boring.