On stage 7, I wasn't counting the secondary fire in missing targets- it's the primary fire that I meant. Perhaps some of the most obvious moments come when you are actually on top of a turret and hitting it, and you make one hit more than is necessary. I know it's not necessary, because for other turrets this extra hit does not appear. At one point you definitely go to the efforto to use your primary attack in sync with the music though.
Another note about it is that the majority of explosions that come after an enemy is killed cause lag. This adds to the total time of the game, and so I wonder if an alternate and perhaps even more exciting way to do this level would be to very closely dodge every single enemy or bullet. See morimoto's gradius run for things which look incredible on such a level. Because this level is so full of enemies and bullets, you will often have the opportunity to pull off similar stunts. The basic summary is to never just stay away from bullets, you almost want to tease them.
I rewatched your arch-nemesis battle and I don't know why I jotted it down as an example of not so good AI manipulation. You hit him as soon as possible, although at one point rather than charging right after one boost, you attack him with your sword and then start charging from that. I wonder if doing this more often would save time? I'm not sure on the exact amount of damage every attack does.
For the boxing.
http://www.thezorz.com/agile/sparksterboxing.smv It takes me about 1900 frames, where it took you 7000, timing both from first movement to last hit. That was done with about 50-60 rerecords, there appear to be a lot more because at one point I accidently held down the quickload button, heh. You cannot expect to do segments with as few rerecords as possible, and you cannot and SHOULD not HOPE to do segments with as few rerecords as possible. You can get him stuck in the corner for awhile(use your lasers more than I did) until he decides to fight back. Or maybe it's even possible to get him stuck in the corner for the entire battle. Something to note is that the turbo toggles only use their specific button once every 2 frames. When he finally gets himself unstuck, after quickloading a couple times I discovered that he would get out either by blocking or by immediately punching, which was decided by which frames the turboed punch decided to pay attention to. If him getting unstuck is unavoidable, be sure to only target one arm, as destroying one arm is all that is necessary to end his obsessive block sequence. The boxing segment of the run alone may take many hundreds of rerecords alone. Do not aim for less.
edit: not to mention that my boxing run was hardly optimized at all. It should be able to be done much quicker regardless of if the enemy can become unstunned.
For the boosts.
http://www.thezorz.com/agile/sparksterboost.smv (edit: link fixed) It is indeed possible to boost one one of the first frames the boost is available.
If your original run for sparkster was 627 rerecords, and the second version was 685, that means a total of 58 rerecords were used in the entire shooting stage onward. This is far fewer than there should be for such a long timeframe.
To be honest, whether a person is awesome at speedruns, or at direct competitive play(as you are judging from the games you listed), it does not have any influence on seeking perfection in doing a tool assisted run. As I said, it is clear that your video game experience helped you to progress through the game very quickly with a small amount of rerecords. But the other thing I said was that the purpose of tool-assisted runs is not to progress through the game "very quickly", but "perfectly", which not only refers to time, but to stylistic components(the three main stylistic components I always have in mind are shot accuracy, taking damage, and boss recovery optimization: if a boss stops flashing with invincibility even for a few frames, it only cost those few frames but it is very obvious to the eye. This is not a concern in sparkster due to the fact that the time it takes to charge is longer than the time it takes for a boss to recover.) In my mind the only difference between an expert game player doing a time attack and an average game player doing a time attack should be that the expert player may have extensive knowledge of the game beforehand. It should have no influence on either the quality of the movie or the amount of rerecords.
I hope this helps, and again I am eager to see any future versions.
edit: where does he get a gigantic boxing machine in outerspace, anyway?
edit: or even...
http://www.thezorz.com/agile/sparksterboxing2.smv
That was less than 10 rerecords, I didn't expect the fight to go like that. At the beginning, I think I hit him barely less frequently and so I guess the game didn't think he was as stuck as he was. That could be improved as well though, as he caught me by surprise by fighting back. But you get the gist.