High action at the nut,high action in general, too much relief, aftermarket parts/screws/nut improperly fitted, improper bridge/nut placement , and tremolo trauma can all be culprits...
-Choose the tuning you use most, your favorite strings, and try and check all of the above.Measure from the nut, to the 12th fret-should be "exactly" half the scale length-again from 12th fret to the bridge-
For tuning to D ( not so dramatic of a drop), you should still be "in the zone" to intonate- not more than an eighth/three-eighths/quarter inch from the scale-( ok, maybe more, but not maxxed out in either direction)
If the precise scale length at the bridge from the 12th means all your saddles are maxed out forward, or back, then you might consider moving the whole bridge-Do you want to do that?
Get a second/third opinion from pros: have it measured, and and if things aren't right, or the tech can't please you, don't go any further with this-
Tune it back to E and sell it to someone as it is.
-If it does check out, have it setup, and proved to you when you pick it up, and before you pay-If it sounds wrong, you are in a position to have it fixed in front of you, and hopefully will be rocking happily ever after...
Good luck from Drac
