If a VIN does not match the registration, if no VIN exists, or if VIN is not on file with DHSMV, the vehicle will be impounded. Then the real headaches begin.
It is a mother to get a new VIN or apply for a lost ***le in Texas. Take the ***le to the county office, get your plates and run it. I've never heard of a trooper or a cop checking a VIN number, if you ever get pulled over for anything short of armed robbery they will look up the plate, look at the car and call it close it enough. Just my experience. If you plan to sell it out of state, well then all bets are off.
Chances of ever being stopped and having the problem come up are slim. Chances of it being a super major problem if it does come up-100% certain. I'm siding with those who say do whatever you need to do now to straighten things out now.
When I lived in Kansas, I built a VW powered trike from scratch. I put the trike on a trailer, towed it to the Highway Patrol office with all my receipts and they gave it a good looking over to make sure it was road worthy. The trooper went inside the building for about an hour to verify my receipts and came back out with a drill, rivet gun and a new VIN plate and attached it to the fork tube. I'm sure the same procedure would work with your car, but like others have mentioned, find out first what the proper course would be. If you mess with the VIN, you may lose your car, go to jail or be stuck with a vehicle that you can't drive or sell. Don't risk it.
Find some Chevy restorers or a Chev club populated by correct nut and bolt types. Since you are RESTORING your car you need some advice on how to rectify the problem. Surely restorers have run into this before.
Right now, you don't own the car - because there's no connecting paperwork or number common to both. You have a ***le that says you own a car - but not that car because you cannot show the original engine (and even then - it's your word). If the state wants to take your word for it (and they may), that's up to them - but they don't have to. Adding another number (the one on the ***le)? You're not altering the VIN at all, and "it was like that when I got it". If they find it during inspection, I think you're OK, if they don't, don't tell them "here's the VIN", instead say "but what about this number here?". Harleys had serial numbers in other places (transmission case and fork crown) pre-1970 (before the frame was numbered) - and they weren't the VIN either.