Ok. For anybody else with the same problem, my terrible solution is to use a bit of in-browser JavaScript. I went to the follower requests page, opened up the JavaScript console, and did this:
<javascript>
count=20;delay=2000; for (var i=0; i<count; i++) {setTimeout(function(){window.scrollTo(0,100000)},i*delay);} setTimeout(function(){$(".js-action-deny").click();},count*delay); setTimeout(function(){location.reload()},(count+3)*delay);
</javascript>
That will get rid of hundreds of followers at a time, which is better than clicking each one. Tested only in Chrome, but something similar should work in other browsers.