How would I go about tuning to drop D without it going horribly out of tune?
A Floyd type bridge is not really made for drop d. Just keep the tuner handy.
So you're recommending not to bother, or to tune it when it goes out of tune?
my floyd is in d. tune the e to a d then retune the other strings. then retune d, then the others----aaaahhhh im going crazy!!!!!!!! but yeah its a pain in the ass. but it can be done.