This is a typical story wherever there's open land to shoot at, BLM or otherwise. Even though I keep my desert spot quiet, plenty of people know about it. When we go out there we pick up as much as we can and burn it in the camp fire.
Problem is, there's to many people leaving their trash to keep up with. It discusses me that gun owners ( not all) do this not thinking of the consequences of their actions. Personally I would like to shoot them for being such idiots. As said numerous times in this thread, these places get shut down because of these idiots!
By bringing in the authorities all it will do is get the place shut down. You can try talking to them and leaving flyers to inform them. Probably get to a few but that's about it. There's those people that you just can't get to listen at all. You can keep contacting the BLM but that goes right back to the same issue about closing the area closed to all shooting.
You can try to get as many of the local gun clubs to come out and do a clean up day. Tell them to bring as many members as they can. This way they can see what's going on and pass it along to the others in their clubs. Hopefully it will help out some but you will always get the dipdunks out there that don't care.
Good luck, hope you can make it work out and cut down on the vast majority of people dumping crap out there.