Ah man, talk about De-Ja-Vu, especially after having had a Kramer that would go through a pack of strings each week, ending the week with 3 or 4 strings still on it.
I always keep an excess of string around the capstans on most of my guitars.
On my Floyd Rose guitars, I just reclamp em' into the tailpiece. Good thing, I break strings on Floyds more than anything else.
Sometimes I re-tie the string through the ball end if I can locate it, I do this on pretty much everything else. Sometimes I have to be careful not to prick myself with the string though.
When I can't find the ball end, I just tie the string through a small toggle switch nut or washer of some sort. Works pretty good, actually, my Jazzmaster has this on the high E right now.