Somewhere on the rear of the PXL case would be good place to drill, gouge, cut, or chew a hole. Make the hole perfectly round and about 1/4-inch ( 7/32-inch for a perfect fit...) round.
Remove the nut and washers from the jack. Insert it into the hole and replace the washers & nut. Now the jack is mounted securely to the PXL case. It might be a good idea to solder the ground wire to the thin washer-like piece of metal before putting it back together on the case.
If you made the hole too small, the jack won't fit through, and if its too big, the jack may slip thru the hole and won't be secure enough.
Now feel free to solder the other end of the signal carrying wire to the inside tongue of the rca jack. Solder back where the little hole is, you wouldn't want to block the recess of the jack from receiving the male cable, would you?