You could always get the suction cups and bracket for the windshield, and put it under your seat. When you get pulled over, as you're getting your registration out of the glove box and before he walks up to ya, reach under the seat and place it on the passenger side floor board with bracket and suction cups seen (make sure their are suction cup marks on the windshield) then just say, it just fell off while I was driving down the road, see? you can even see where the suction cups mark were?
Then you're clear!
Of course, doesn't it seem odd that states haven't stepped into this century? Why don't they offer printed out PVC (think fat head material) adhesive plates that have enough contrast to make out the numbers, but enough flexibility to where the tag doesn't destroy the aesthetics?