Zayne,
Sounds like you are about to go through hell.... welcome to CA, I guess.
When I was still living in CA, I bought a '69 K5 tub from a guy in Arizona (no frame)..... I got a bill of sale and no title (just like you) and called my local police department (not CHP) to do a "VIN Verification" on it. The guy was really nice and checked the VIN tag and filled out his paperwork. Obviously he didn't have a frame to look at but it didn't seem to matter all that much. I got his completed documents and took them to DMV and got it registered and titled.
If I were you, I'd try to find a friendly local PD guy to work with you on this. Obviously, this is a 50-year old truck..... it's not like there's a HUGE market for "stolen" Blazer parts so it seems ridiculous that they are scrutinizing the frame stampings, cleaning off paint, etc. and looking for some kind of nefarious plot or crime. The frame may very well have been swapped for a nicer one at some point.... the 1972 frame was a 1-year-only design with turndowns at the front and rear sections that allowed the bumpers to bolt on directly. 1969 - 1971 had a more "blunt" cut of the frame on both ends. If the truck was in an accident and was severely damaged it probably would have made sense to swap in a "used" frame vs. trying to salvage a really bent one.
In any case..... I'd find a local cop who is more willing to work with you. If they want you to swap in a "correct stamping" frame and they are strict about it, you CAN still find them around. Being in LA, your odds are better than most. There is a shop in Fremont CA that sold me a really clean and complete 1971 frame for $500. I'm sure you could find a place that specializes in old Chevy trucks that might have a stockpile of old, straight frames. The main thing is to keep working with that same officer throughout the process..... if you find a good "donor" frame, take photos of all the stampings and show them to the cop..... make sure it's what it required for him to signoff on the title paperwork. You don't want to waste your time doing a frame swap only to find out that he STILL refuses to sign off after all that effort.
Hopefully the body is in good shape so that it's worth all of this effort.
-G