So, turns out the input smoothing I was seeing is actually a Dolphin feature, not a feature of the game (thanks for the help, JosJuice). Using an older version of Dolphin makes it much easier to do precision captures. Also, this time around I managed the camera a bit to keep the game running at 60fps. It's still not perfect--for some reason, even when it's not lagging, the game seems to drop inputs occasionally. Not sure why that happens. Regardless, this version looks much cooler with entire swaths of Elebits getting cleared out super fast.
Link to video
(aka Eledees)
If there was any TAS I could wave a wand and magic into existence, it would be Elebits. I think it has a lot of potential: interesting routing, camera management, that ordered chaos of capturing Elebits at ~15Hz, lag frame management... and I can't even begin to imagine all the wacky things a TAS could do with that physics engine.
I don't think I personally have the patience to make a TAS, especially with the current state of Dolphin's TASing tools, but I did do a minimum-effort PoC (didn't even do any re-records) just to show off how cool capturing Elebits really fast can be:
Link to video
But you know, I already realized that this obvious strat isn't actually optimal. Turns out the game runs at up to 60fps if there's fewer things on screen, so if you turn the camera towards a wall you can capture Elebits at 30Hz instead of 15... at least in theory. The problem I run into trying to do anything more complex than just spam-clicking clusters of Elebits is contending with the game's input smoothing. I almost feel like it would take a script to efficiently capture Elebits even on a simple stage like this one...