This game lags 2 times every 3 frames, so for the sake of my sanity when splicing, I took account of the lag frames. This unfortunately makes it look like I'm button mashing, but...
Improvements
Menus
Saved 65 frames optimizing the menus before the first stage. Any frames that don't add up from the savings below will also be assumed to be from this.
Stage 1
Turns out bouncing and getting the burger ends up being slower than what this TAS does. Even with optimizations, the route the current run takes is 39 frames slower.
It's 18 frames faster to stop shortly before the white claw and jump than it is to jump once more before hopping on the basket. This number also takes account to optimizations.
Avoiding taking damage saves ~15 frames since getting back up kills off any gain from moving 7 pixels every 3 frames.
I used the bag to hop towards the sock by the ironning bar because bactracking costs frames.
Previous TAS - 5554 frames
Current TAS - 5127 frames
Saved - 269 frames
Stage 2
For the first large crate I had to jump on, I had to position myself so that I won't get shot as soon as I leap off it. Leaping off the alcove is faster than continue to run.
I lept after taking damage as I would be forced to stop otherwise. I tried to avoid the gunner, but I wasn't able to.
Stopping early before jumping to the 2nd crate ended up being 3 frames faster than having an extra leap before jumping.
For the green roof at frame 7920 however, it's 21 frames faster to leap before jumping due to the wall immediately stopping your movement, allowing you to jump.
The gunner inside the "INBARRR BLACKSMITH" building is triggered as soon as your x position goes past 3227. I had to stop there or else I wouldn't be able to both recover and leap past him before he shoots.
I used a different way to get the money bag before turning to manipulate the shooter on the roof to damage me in order to cancel the landing animation, saving 3 frames. I tried implementing the way the current TAS grabs the bag, since it save 6 frames, but it caused worse behaviour for the gunner; he would shoot too early, so as I land he would've retreated and not be able to hurt me.
Previous TAS - 4246 frames
Current TAS - 4030 frames
Saved - 216 frames
Stage 3
I tried to find a way to get all the markers without doing a lap, but apparently, they only respawn after going 1 lap clockwise. Pressing Up/Down here does nothing, while Right/Left turns the boat.
From my testing, it seems going out my way and getting all the fans ends up being 6 frames faster. As much as I tried improving, I keep getting the feeling it may be possible to save time somewhere, but not sure.
Previous TAS - 4336 frames
Current TAS - 4309 frames
Saved - 27 frames
Stage 4
Yet another driving stage. This time, you ride on a toy car to collect 10 wrenches before you're allowed to leave. I found out here the hard way that it's 6 frames faster to turn completely at the very end of the intersections rather than gradually turning.
Oh, and I found out that if stay at the top part of the road towards the goal (Y position < 882), you simply go past it as if it wasn't there. I can't seem to find any use for it at the moment though.
Previous TAS - 5048 frames
Current TAS - 5162 frames
Saved - 114 frames
Stage 5
You know something's not quite right when a platformer game has most of the game devoid of platformers. Thanks to the linear style of this stage, it was the easiest auto stage to do.
Previous TAS - 3310 frames
Current TAS - 3208 frames
Saved - 102 frames
Stage 6
Because what you expect from a platformer is driving right? Also, because of budget cuts, rather than have parts of the bridge had to be painted with the color of natural rain rather than wood.
Previous TAS - 5525 frames
Current TAS - 5318 frames
Saved - 207 frames
Stage 7
At the beginning, it seems leaping 3 times is faster than than leaping twice then running. Also, I delayed the leap to the spider so I can cancel out the landing animation to save 12 frames.
The 3rd coin in the published movie becomes the 2nd coin here because back tracking is bad. I won't blame the previous run though; apparently there's only a small area where this is possible, so it's easy to miss.
This single toad gave me a ton of trouble. I tried to see if taking damage from the frog unlike the current TAS (since that allows me to jump immediately) would be faster. It ended up me having to TAS the entire level after this point twice, since it messes up 2 critical points later. The first is that it forces me to grab the health BEFORE getting the token, and the second is that I had to wait out the steam pipes before the last health pickup. Taking damage here ended up being 24 frames slower in total.
The steam pipes gave me some trouble, since I only had 47 movement frames before I'm vulnerable again. Thankfully I was able to manipulate my landing so that I could leap past the area nonstop.
It seems your jump is just high enough to make it to the top at the first platform. Who knew?
For the backtrack to the 6th coin, it ended up 3 frames faster to take damage from the spider in the air rather than slow down and take damage from it on ground.
Hopping to the higher platform, before leaping over the toad like the current TAS is 3 frames faster than landing next to the toad and jumping over.
Now you may noticed that I paused to avoid that spider. I'm aware of that, and I even tried using the same route as the current TAS (not taking damage from the toad before hand). It ended up being ~70 frames behind + still had to wait regardless. It was only due to the steam pipes that I stuck to the published movie's route.
For the last coin, it seemed the only reason why the coin isn't there was because of too many objects on screen. Moving slightly left fixed that.
Previous TAS - 8257 frames
Current TAS - 7436 frames
Saved - 821 frames
Stage 8
This is the final stage.
It seemed leaping to the branch with the bat is faster than running/stopping by 12 frames.
I had to delay 3 frames before entering the hole or else the note needed would not appear.
Due to manipulation, I didn't need to heal unlike the current TAS.
The delay before grabbing the last notepaper turned out to take the same amount of frames as grabbing it like the published run. :P
Previous TAS - 7763 frames
Current TAS - 7036 frames
Saved - 727 frames
Possible Improvements
Potentially all stages can be improved with better sub-pixel manipulation, especially the drive/sailing stages.
Better enemy manipulation for stage 2 so that 9 frames in total could be saved rather than 3 from that gunner.
If someone can find a way to mess with the game using the OoB glitch for stage 4, that would be nice.
Further lag reduction seems possible in stage 7 in the parts with the steam pipes.
A better route for stage 8 as to not need to backtrack too much would help.
Tricks & Glitches
Stopping immediately
Normally after running, you'll skid a bit before standing still. By stopping early in front on a wall, it allows you to instantly stop; which also allows you to jump immediately.
Cancelling landing animation
By taking damage at the same frame as you land, it cancels the land animation and allows you to move right after.
Clipping into blocks
If you get stuck into a wall/block far enough, you'll be pushed up rather than away from it. Its most noticeable application is during stage 1 at the beginning (discovered by NitroGenesis) and stage 7 on the way to the 5th coin.
Out of bounds in stage 4
For some odd reason, they never bothered to check the top part of the end point whether you pass it, allowing you to go past it.
Addresses
feos: Replacing the movie file per author's request.
feos: Accepting this improvement over [2576] GBC Stuart Little: The Journey Home by Fog in 12:50.57.
Fog: Processing...