I frankly don't believe there are that many Vins or partial Vins on these cars. I believe you'll find 2 on the body, one on the engine, and one on the trans. And I don't believe police officers are anywhere close to being the experts on this topic. There are so many cars of so many eras and origins with so many varying VIN locations...

Here is a nice photo breakdown & explanation of where they are found on 1st gen Camaros, and how to ID them. FGF's will basically be the same:
http://www.camaros.org/numbers.shtml#PartialVIN

You'll also find that the states vary widely on how easy/difficult it is to get an assigned vin or swap a vin. In Indiana I've applied for VIN's several times and had absolutely no problem or hassle getting assigned DMV vins and titles for several vehicles. I have obtained assigned VINS (because I didn't actually have a VIN to swap) on a boat, a trailer, 2 motorcycles, and 3 different cars. And I've also dealt with lost/misplaced titles twice on cars personally (and about 15 times a year professionally as a claim adjuster who totals cars often and disposes salvage) and I have had no problems getting good replacement titles with the original VIN in exactly 100% of circumstances. But in every circumstance it involved a bit of a process. First get an app from BMV, then having police out to the vehicle (or you bring it to them) to inspect the vehicle you want to title...they look for ID markings and run them thru a database to confirm current ownership and/or stolen status, then the cop signs off on it, and then the DMV confirmed or gave me a valid and/or assigned VIN in assigned for that police verified app. If it already had a VIN, process over...title comes in the mail. But for the assigned VIN vehicles the DMV first provided me specific instructions of where I should stamp/engrave the vehicle with the VIN they provided, then the police had to come back out and inspect AGAIN to make sure I applied the VIN in the correct size/location/method per BMV instructions, and then I sent in the final form to DMV and a title showed up in the mail a week or two later and I was legally the owner and on my way to get them licensed for the road/water. Obviously these assigned situations were generic VINS, and from a value perspective this is something to consider. But you might not need an assigned VIN because you already have vins on 2 cars. You might need nothing more than a VIN verfication and theft database search to get a replacement title for the shell you're buying.

I haven't heard this asked yet, but does this beautiful shell you're looking at come with a title? This should be your #1 question as it solves EVERYTHING. If the answer is no, HUGE red flag...ask owner why not, and then verify their story with police/DMV prior to your purchase. If it can't be verified, walk away because you might be buying a body shell from someone who is not the legal owner. If it has a VIN and simply a lost/unknown location of title, you can probably get a replacement title for the shell and avoid the whole VIN swap easier than you think, but you MUST run a VIN check on it before you buy to see who, if anyone, is the current titled owner of the body you're buying. Somebody is, and hopefully it's the person you're buying from. If not, you will need to find the titled owner and try to get signatures and/or death certificates for that person. This complicates things, but again I've gone down that road and if it's not a stolen vehicle it has always worked out for me in the end also on the salvage side of my career.

Getting the valid title for your replacement shell somehow/some way protects you from buying a stolen shell, and the seller from selling a stolen shell. If you can get a title from the current owner, or apply for a replacement for the lost title for that body, then there is no need to swap vins and this whole discussion is moot.

So regardless of what method you use to title this car and move/leave VINS, the only true resource you're going to really have on this whole topic is the DMV in Oregon...not anyone on this site unless someone here who lives in Oregon has done what you're talking about doing. They're the true experts on titling issues. Contact them, explain your situation, and get their written procedure and forms/applications prior to buying this body. This will answer all your questions.