I've finally, after many months of grappling with it, managed to figure out what was holding me up from disabling the Platform on Facebook.
Turns out ages ago I made a blank app, in order to be let into the "timeline preview" for developers early. While it's my fault, I still feel entitled to whinge because of the utterly abominable and completely useless error message you get when attempting to turn off Platform. It seriously might as well have said "NO!" rather than anything else - aren't error messages supposed to at least hint as to why something didn't work?
Anyway, once I deleted my "fwaggletest blank" application, turning it off went without a hitch. I didn't have to click it multiple times, or anything like that (probably because at this point I have no other apps on my profile). I'm finally free of all those incessant application invitations, and of Facebook showing up on all sorts of 3rd party websites.
I realize of course that folks posting via some applications, I won't see their posts - but that's a small price to pay. If Facebook would simply get with the program and let you opt out of some parts of their platform while still letting you use the rest, I'd be happy to do so.
Another part of me is just waiting for it to die so we can move on and use something else instead. Google + looked promising, but in addition to not really reaching critical mass outside the tech circles it's also heading in the wrong direction on some fronts.