Finally, a good temporary (and perhaps partially permanent) solution. I finally figured out a way to speed up the site (I think). Though I, of course, have "top-secret" "internal builds" of the website system which do run faster, I do not have time to finalize them, seeing as I am starting college tomorrow. So, I must instead make do with a much quicker and dirtier solution, which, in fact, many other sites use.
Instead of keeping the site always perfectly fresh, I have put a one-hour cache on it. This means that the server won't even try to generate the page at all for most requests! (For editing, I've made a separate site which is not thus cached, and it takes the full amount of time to render - sometimes .15 seconds, other times (if the server is running backups at that time, which uses ~100% CPU) over 20 seconds!).
I am a bit irritated, however, as if the CPU and memory of the server I am using were sufficient I would not be having most of these problems.