Basically you were right by assuming that it's being caused by going back and forth between drop D and standard tuning. You may not think there is a huge difference in string tension between D and stanrard but in terms of ft/lbs it's quite a lot... I can't remember the original number... But I wrote a mechanical documentation of one of my guitars for my Technical Writing for Engineers class last year and I had to include all the measurements for any stored energy... blah. blah... boring............
Anyway... Another common problem with Floyd Rose style guitars is the locking nut.... Most guitars have the force of the string pull dispersed through 6 different tuners.... With a Floyd Rose, a small amount of string pull is located at the tuners... the rest of it is focused at the locking nut... Giving the strings much more leverage to cause a bit more bow in the neck... They say that Strats are the hardest instruments to set up becuase they're so finicky... but I say that any guitar with a Floyd Rose is the hardest because the set-up could be right today.... and completely wrong tomorrow after everything settles in. It's hard for me to say exactly what is causing it because I can't physically inspect the guitar... But I'm guessing it's just from going between D and standard tunings... Maybe check out getting a Trem Setter or something similar to help balance the trem....
One thing that I do is set my guitars up for specific tunings... I have a few guitars setup for standard and a few setup for drop d... and in no cicumstances do I tune one to the other... This ensures that my guitars always play the way I set them up to play... I understand that not everyone has multiple guitars... and that's fine... Tuning between drop D and standard is really common and isn't going to hurt your guitar... It will, however as you've seen, cause you to have to get use to different playing conditions.
Might want to take it in for another setup and let the tech know what's going on.
