We replaced all of our stoppers with screens since we have a wash tub for dishes. Didn't do it necessarily for this particular reason, but now that I've read this I'm even more glad that I did.
Good that you caught it quick and got it cleaned up.
Our first time out I went over my checklist ten times and still got distracted and tried to jack the trailer up to hook to the truck with the stabilizers down.....luckily I noticed the sound of our tongue jack change and realized what was going on before destroying the rear stabilizers......it's a learning curve