Here is the way I figured out mine was somewhere close to number 950. First, keep in mind that the VIN includes pre-production and pulled-from-release XLRs. So, it is not a good indicator of the total number of production-level XLRs.
Once a month I get the official GM numbers for production and post them on this forum. I also used to get Autoweek weekly estimates, but really the monthly numbers will help more.
For your vehicle, you'll need to know when it was produced and ready for shipment. There is probably a few days slack in that date, so you can only do an estimate.
If you have that and then the total number produced at the end of the month of production, you can estimate where you're XLR fits in the queue.
At this time I can't confirm or disconfirm your anticipation of 2,700 XLR units. But stay tuned someone out there will respond. I will attempt to get with my sources in the next few days and let you know what I learn.