I should have been more specific. Not on the tunnel, but on the engine case itself. On the recoil side rear portion of the lower case you will find the engine vin. That is where the punch mark may or may not be.
As you found out, Yamaha no longer keeps those records on hand, but, if you happen across the dealer that sold the sled and perhaps did the warranty work, they may still have the info on hand unless they have changed ownership since.
Your looking for the proverbial needle in the haystack unless the girlyou bought from was the original owner, then that will narrow the search a bit.