Phil...OK....I understand, first advice I'd have...do NOT fly in extreme sandstorms...!!! [G..!] But, beyond that, what I suggested would still work...just use a UV or an optically clear filter of the correct size and affix it to the inside of the lens cap...(after cutting a hole in it....duh)...!! And...depending on how tight a fit it is...or how brave you feel, a few pieces of tape would provide some additional insurance. You might find it easier if you removed the threaded ring from around the filter itself, that would allow a snugger fit and might eliminate any vignetting that could occur due to the extreme wide angle lens of the Phantom. And...since the lens cap is now useless for it's original purpose, you might as well glue the filter permanently in place.
Check the Bargain Bin at your local camera store for cheap clear filters in smaller sizes. I just measured mine and it looks like something in the 37-38mm range might work. Not many of the current cameras use these smaller sizes, so you might find something for just a few cents.
Good luck...