First, the guy at the parts counter is just being lazy. Yes, it's easier for them to look stuff up with a VIN, but it's not impossible to do it without. Especially after you tell them why you don't have a "correct" vin, they should be able and WILLING to find a way around the problem for you (the customer). If they really insist on having a VIN, they could go throught their own customer files and find an appropriate one to use. After all, you're buying what I'm assuming is an insanely overpriced rear from them; they should be bending over backwards and kissing your ass to sell it.
Which brings me to my next point: Why on earth are you buying a complete rear from the "stealership"? A used, low mileage diff would be much cheaper. Try the junkyards (sorry, "automotive recyclers")/ebay/craigslist/etc... For that matter, it would be far cheaper to just put new gears and a L/S in your existing diff, and you could do a full professional rebuild, and still be ahead of a complete new factory rear.