No I haven't even seen the other stages of the game honestly, I never got past stage 1 as a kid so that's the only one I bothered to look into.

3:36:XXX possible in TAS I'd say, but I'm not dedicated enough to do it. I whipped this up in about two hours, and it's spotless. Incredible work though, I didn't expect the old TAS to ever be beaten, not unless a new major trick got discovered. Considering there's like 5 people who even remember this game though, it probably isn't likely we'll be finding new tech anytime soon. Here's to another 2 seconds.

Upon further investigation I believe the "speed" number, while displaying as higher, isn't actually making you move any faster. In fact it's more beneficial to get it down to 580 more quickly because that is the only number that passes the check for the game allowing you to build turbo. Basically, it seems useless, but I could be wrong, I didn't test it very thoroughly.

I can confirm it works on the US version as well. And it does appear to retain the higher speed while allowing for regular turning, could be very useful if applied correctly.

So I noticed this new WR run (even though it's 8 years old) has a potentially useful trick in it. Skip to 1:57 and look at how he's shifting to retain booster speed. It could just be a visual trick but I'm not sure, could be something interesting. I have no idea where it could be useful but I'm going to attempt it on the US cartridge.

(Current WR?)

I've done some experimenting with TAS and I recorded 2 separate TAS runs. One using the R3R5 route, and one using R2R4. I was surprised to see that R2R4 was faster, but going by the segment times the optimal route APPEARS to be R3R4. Here's the clips. Both of these were done on the US version of the game.

R3R5:

R2R4: