Thanks for the advice. I'll probably go ahead with that, actually. I'll just have to think of something appropriate to use as a subdomain.
Incidentally, a friend of mine suggested an additional option to me. They suggested that I set my MX record to point at my email host, and then point the rest of the TLD to my Linode. To get my alternate host to cover the web as well, I could set up a simple permanent-redirect directive in Apache or something similar.
However, coming up with a subdomain is probably for the best. You're right; there'd be a lot of crazy routing to do, and while it'd be fine for some purposes, I need reliability with minimal administration. (Hence leaving my web service in the hands of a host that "does it for me", such that I can concentrate solely on the software I'm writing.)