Here is a good historic read on the Titan Swap:
http://www.thenewx.org/forum/showthread.php?t=14761
Look at La Rana's post #65 where he mentions the specific part numbers. You don't need a VIN to lookup a part number for the diff assembly.
There may be updated information, as this is from 2009-2010, but a dealer could at the very least cross reference using the numbers in the thread above.
Another option is to use the Search feature on this site and search for Titan Swap in the thread title. There are a lot of great posts about the Titan Swap on this site. Some of them will include the part numbers, and some will not, but many will have very useful information.