Well, there's good news and bad news.
Good news: Last night I figured out how to solve my problem (thanks again for the help, but my knowledge of calculus is miniscule, so I'd end up researching a lot more of those terms than with this homebrew which is, probably, the same damn formula. I don't eschew knowledge, I just want to finish this thing ASAP) by scribbling all over a piece of paper for several hours. I got to bed around 5.
Other good news: Flare, for one, because I honestly think it could have some interested repercussions. Lots of neat stuff could be done with Flare that would have a natural storage solution with XML data storage, and lots of neat stuff could be done with existing XML data as Flare data structures, IMHO.
I'm not smart enough to do it -- yet -- but I will be, dammit. Flare. I can't say it enough.
So, my next step here is to code the rest of the solution I whanged out last night and then start refactoring, assuming I can make the solution work immediately. My main problem is one that I believe was discussed in the assistance one diary entry provided, that of curves with two intersections with the average point and no more. (The two "end" intersections don't count for my purposes, so I need to figure out how to make sure there's a middle, and my model doesn't cover what to do if there isn't one.) I'm considering a few attempts at proving it's possible, just to make sure that this is something I should be worrying about. (With my incoming data, it probably isn't. The truly worrisome case I could see is where there are MULTIPLE points past two, seven or eight averages in the middle that I need to worry about. Sigh.)
So if this doesn't pan out then I'm going to take the tougher plan and figure out a way to bisect it, which should provide the results I need no matter how many "average" points there are. Goddamn modes.