So I just did my semi-annual "log in to Twitter to see if it's any good yet", and found that in my absence I had followed a few thousand new spam accounts.
Sweet. That explains why they emailed me and forced me to change my password last year.
Being Awesome, Twitter doesn't have any way to simply toss out all your followers and start from scratch. And none of the spammy apps claiming to do so actually will (even seemingly after charging you money to try).
So instead, I just pulled open the Dev console and did this:
setInterval(function(){$(".following").children("button").click();window.scrollBy(0,5000);}, 1000);
Figured somebody else might find that useful. Enjoy!