If you don't use the trem, I would suggest blocking it somehow. There are several solutions to accomplish this, some simple and cheap, some more elegant, some more permanent, and some simply more effective than others.
In the rear spring cavity, anything you can wedge in between the body and the bridge to prevent it from moving can be effective. I've heard of people custom cutting blocks of wood to serve the purpose, which would certainly be preferred, though might not be easy for anyone to do. I've even stuffed a nine volt battery under the rear of a recessed bridge then added extra springs to essentially fix a floating bridge in place, which worked reasonably well.
There are also devices you can purchase to serve the purple, such as the Tremol-no
. Some people swear by these things, though others (including myself) have had mixed results. If you were to tune to standard and get the trem fully set up, then lock it with the Tremol-no, you could make relatively small tuning adjustments without going out of tune. For example, drop-D would be no problem, or the whole guitar down a half step should work well. You would not want to remove all of the strings with the Tremol-no locked, that would likely be too much stress for it to handle, but otherwise it might be a good solution for you.