First, there seems to be an emblem mounted beneath the big "Shasta" emblem. Shasta did not put model names on the trailers, like car manufacturers did, until the very late 60's and early 70's. I can't make out what it says in the photo, but if it is even partially there, it would be a huge clue.
Second, do NOT take a grinder to the paint to search for a VIN number, a wire cup brush in a drill or Dremel tool work well for removing paint and revealing the VIN. The numbers are stamped into the metal on the tongue and can be easily obliterated with anything too aggressive.
I'm going to go way out on a limb and take a wild-assed guess. It doesn't appear it is a Starflyte, Ultra, or Super, all of which had some version that included the trunk back. I am thinking that it is the 19' Deluxe, judging by the window layout and the apparent length. It is only a guess though. I'm still looking for definitive proof for you. If you have any photos of the interior layout before the remodel that will help too.