Everything about the glitch that triggers the credits, done via item swapping a Chuck by collecting and licking a coin at the same time, is described in the submission text of the previous movie
. Thus, I'll describe here just the improvement itself. Instead of eating the green shell right after spitting out the fireballs, I kicked it forwards by touching it while Yoshi is ascending. So, it's possible to spit out the fireballs much further before getting the green shell. This initially was saving 4 frames, but after a while it was possible to save 8.
Amaraticando, then, managed to save an extra frame, by spitting out the shell while Yoshi is turning right. That, however, was preventing us to get the credits, because the controller #1 register ($4219), which allows us to trigger credits with input, wasn't being executed. We investigated a lot what was causing it, and it turned out it was Mario's position. At frame 2510, $4219 is not executed if Mario's x position is 2470 or higher, in this situation. Therefore, we have to press X and left at the very end, before the game end input. The last inputs that trigger the credits were done by Masterjun.
Update: The berry, placed where we needed to be to get the green shell, was stopping Mario for a while. Berries freeze Mario's position a bit when Yoshi eats them with his mouth, but the rest of the game keeps moving (such as the fireballs). Avoiding it, however, seemed to be impossible, because we had to press < to not destroy the shell, and that makes Yoshi to turn around and eat it. The solution was to turn left before, and then turn right at the very moment we spit out the flames. While Yoshi is turning right, pressing < doesn't make him to turn left. This way, we could spit out the flames even further, since it's easier to catch them up without the berry disturbing us.
There's a frame rule that affect the fireballs: they can turn enemies into coins only in 1 frame out of 4. And this frame rule was horrible to us, because we would need to eat the coin at the same frame it turns into a coin, which means it is still moving with the shell's speed, which is too high. It was obligating us to dismount Yoshi only in the upper platform, but that, again, was preventing $4219 to be executed. The solution was to spit out the flames much below, and spit the shell at a very high position, so that it takes 4 extra frames to be burned. In this 4 frames we spit out Yoshi's tongue and dismount it in a proper position, and both Mario and Yoshi's tongue reach the coin at the same time.
: Replaced with a 1 frame improvement.
: Accepting as an improvement to the published movie