Two interesting points of note:
* The touchspecial sector flag seems to actually do its job now.
* Detection of sectors with polyobjects in seems to have done this incorrectly, but this doesn't mess with anything about touching the polies themselves so it seems to really only handle edge cases where the polyobject was too close to the border of another sector (which would've likely made rendering glitches anyways).
* There was a whole swathe of teetering code that was basically never run properly because of this mistake. I did a simple fix at first, but you started teetering whenever you were slightly less than your radius away from a sector's edge, which was completely different and undesirable behaviour. Instead, I cut out the code that was never running, and just left the hacky method in instead since it was more accurate to what we want in general.