!!! Someone's finally TASing this, god bless your dear soul!
I did a speedrun of this, sorry about the wretched quality though:
https://www.twitch.tv/phwoom/v/49252546
I expect a TAS to be around 19:30ish for this game. There's very little in the way of TAS-only maneuvers that can't be implemented in speedruns, at least that I could find. No time-saving glitches either, though there are a couple you can show off for entertainment.
Some notes about your WIPs:
WIP 1:
1:17 - Nice route here, hadn't thought of this.
2:11 - You can indefinitely keep the two enemy cavemen on screen by repeatedly landing on them from above, which causes them to flash with invulnerability and stop moving. Shortly before the triceratops is set to stop moving the cavemen will kind of automatically slide off screen. If you jump onto them as they're doing so, occasionally their sprites will glitch out, but it seems random whether this happens or not to my eyes.
2:33 - This is the only glaring mistake of the WIPs. Any time the game freezes Joe's movement to slowly center the screen on him, you want to absolutely avoid being at the edge of the screen and instead be centered on the screen on the frame this process is initiated, ideally having started sprinting a second or so beforehand.
2:36 - Looks like you might've been able to jump a bit later here before walking off the triceratops' snout.
Also, this is just a suggestion, but entertainment is a bit weak during the autoscroller segments, of which there are many. This game is about as straightforward a platformer as you can get, so entertainment during downtime is paramount.
WIP 2:
0:15 - There is a visual glitch you can activate here while hanging on a rope. When Joe reaches the left edge of the screen, he will be pushed off the rope; when he is about to fall off, swing your club and he will remain airborne hanging on thin air. You can keep him airborne indefinitely by doing frame perfect club swings successively. Use this for entertainment how you will. (Perhaps you could even keep Joe suspended at the top of the screen and get a faster dropping speed into the cavern to save some frames?)
0:55 and 0:57 - You can turn around quickly by depressing the dash button as you reverse direction on the D-Pad. It should save some frames here.
1:16 - I suspect your method here is fastest, but there's an alternative where you refrain from clubbing and simply jump as late as possible without getting hit by the first caveman. You grab the rope a little lower but forgo any time loss from having to swing the club (maybe there is no time loss while on icy floor?)
1:35 - I expect that you tested whether ducking or clubbing here was faster.
3:08 - This doesn't look optimal to my eyes.
3:24 - If you jump a bit later here, you can still clear the bouncing shell but also land on the caveman's head, forgoing the need to club him.
3:44 - The platform extends far enough here that you can run underneath the first bug and jump without hitting him. I believe you can in fact land on the propeller-suspended platform without needing to grab a rope along the way.
4:04 - You can abuse the same visual glitch mechanic as with the avalanche autoscroller in the snow stage. When Joe is being pushed off a platform by the left edge of the screen you can club indefinitely to keep him airborne (not sure how this interacts with the giant pterodactyl though, I believe he sweeps you away regardless).
4:58 - Not sure why you take damage here, it's very possible to get 4 hits on the first phase without needing to do so.
5:42 - Again, you might be able to do a faster turnaround here.
Thanks again for taking on this project, I'm really looking forward to the finished result! I'm going to be away from home without internet from tomorrow evening until May 1st but after that I'll be sure to check any additional WIPs.