You gotta start by being honest with yourself. Are you only interested in this car because it's an AAR? Because without a VIN or with a state issued VIN it's not an AAR. It's a Barracuda with some interesting options. Kinda like a Cobra kit car Vs. a real Cobra. What makes the AAR so valuable and collectible unfortunately is documentation. The more documents you have proving what it is, the more it's worth. With no VIN you can point at body stampings and pitman arms all you want, but that doesn't prove anything to anyone who is willing to pay for an AAR. So as it sits, its a 1970 Barracuda with no engine, transmission or VIN. You will have to jump through firey hoops to prove you own it, pray it isn't stolen and fill out a ton of paperwork and be rewarded with a random state number saying you own it. Then you can restore it to look like an AAR but without documentation, it will appear to be just a clone.
This is all assuming the missing VIN hasn't been reused on a "rebodied" car. Now picture this scenario. The guy with the tags buys a mint 318 Barracuda and gives it the full AAR treatment and puts the tags on it. He now has illegally modified a car via VIN tampering, but who would know except the owner of the original body? And what happens if you go to the DMV with a VIN determined from the body stampings and their search shows that same VIN in use in another state?
As I see it you have two options: Buy it as a 70 Barracuda, pay a reasonable price based on THAT value and begin restoring it. Keep tracking down the original VIN tags in hopes they can be reunited. Or 2, pass for now and hold out for what you really want that won't require all that paperwork. Either way, the restoration costs will be the same:astronomical!