First off, I loved the arcade mode TAS, you should make another one that goes for the highest score possible. I'm sure you could max out the scoreboard with a TAS and the infinite reverse backdrift.
I would love for a Crazy Box TAS to happen, but you really have to consider what you want to do for this category before working on it. Are you doing a single video for all the levels together or a segmented TAS for top scores/times for individual levels? I would assume most people would want to see the latter, but just make sure before you start working on it any further.
I ask because it is faster to get as low of a score as possible in Crazy Jump, but obviously that is not as impressive. It is also faster in a complete run to stick with just one driver, since switching drivers costs ~2sec each time, but certain drivers seem to be better than others for some levels. Plus the bike is much better than the cab for most of the levels, but there are a few (1-1, 2-2, and maybe S-S) that the cab performs better in. Would you stick with one or switch drivers to whatever is most optimal for the level?
Maybe these answers are obvious, but I just want to throw them out there as this game can be tough to categorize and I really want to see Crazy Box get a great TAS video.
This video
https://www.youtube.com/watch?v=0ljK8nCGKq4 is the furthest distance with video proof that I've seen for Crazy Jump. He is playing on the xbla version, and I feel like there are some small differences in the physics system between that re-release and the DC/GC/PS2 versions, but that could just be me.
I'm not great at 1-1, but from experience it seems kind of luck based, doing the same timed inputs seems to give me varied distances from low to mid 300. When you switch gears between drive and reverse, one end of your car will raise up slightly. This is probably to lessen/increase the friction between the tires and the road while boosting/braking. Poorly timed boosts where you switch too fast between gears can cause your car to rock up and down and lose speed. You want to time your limiter cuts so that doesn't happen, and do 2-3 of these down the ramp, then 1 more as you are climbing up the final curve. Also, the bottom curve of the ramp seems to not be completely smooth in places and you can easily lose some speed by limiter cutting at the wrong time and essentially hitting part of the ramp with the front of your car.
Also the 2-2 video that was linked is mine, and I just recently discovered that the psn leaderboards for Crazy Taxi has a 14"69, so its only the best with video proof; however, that gives you a general idea of the fastest route for that level. I'm not entirely sure how barrier boost (the wall glitch) works either, as it happened by pure coincidence while I was testing my capture card. This game has very strange collision detection and more research needs to be done on it. I would love to test more myself, but my PC cant run dolphin very well.