If you’re breaking strings just going from E to D on the low string, there’s another problem. I need to do a tuning video for Floyd-based guitars. Lots of folks here seem to need it, so I’ll try to get that done this week.
In short, the fine-tuner on the Floyd should be close to all the way screwed in when it’s tuned to E, then just unscrew it until that string is at D.
Because it’s a floating bridge, all the other strings will now be sharp, which is why it’s not easy to change tunings on a floating bridge. If your plan is to go from E standard to drop D and back again a lot, you might want to look into having an EVH D-Tuna installed.