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I made this TAS to see if I could get the 5.57, and yes, I just got it! I am completely blind, so I had to take a screenshot and open it in Chrome to check the final times for each attempt.
After general testing and experimenting, I managed to come up with a strategy of my own to achieve a 5.57. I did this from scratch with no real resources to go by. It took me just a few minutes before the mathematically proven best possible time appeared on screen.
Completes the race in 5'57, the fastest I could manage. I don't see how to bring this time down, unless a much better way of shifting gears is found or you can get the speed up faster than 2 every 2 frames.
calfd mentioned this game in Atari 2600 Wishlist, so I decided to give it a try. This time is 1 timer increment faster than the best Scoreground time, but 18 frames slower than the 1980 WR.