Cartier Transmission Shifting all gears immediately!!!!!

I have a 2003 Lincoln town car cartier. We matched the vin with a junk vehicle we had to make sure the transmission was interchangeable. When we installed the transmission the car would barely move and in diagnosing and talking with experts of the vehicle line from identifix we found that the ring gear teeth in the rear secton of the transmission turned out to be completely different and that is the only issue or difference between the two. The one has 24 slots and the other has 6 big holes. The speedometer is reading 10mph but with the tools hooked up the speed sensor is reading 55 so just pulling forward the transmission is shifting threw every gear causing it to not move and it is automatic obviously. The VSS output speed sensor is what reads this and causing the issue well without getting another transmission is there a way to make this transmission work? Some sort of program or update that we can do to the car to get this thing to realize the difference? According to the dealer this was supposed to be exact interchange with no issue what so ever and this is the only one we are having but have ran into other vehicles where you can do some sort of learn or possibly maybe a different type of sensor. Can someone please help me with this would be very greatly appreciated our shop is a aftermarket shop and we do all makes and models of vehicles so we have almost every scan tool that is out there all up to date and most of the dealer tools as well we have for instance with this line would be the IDS. Thank you in advance and hopefully someone can help with this issue so we can get this taken care of im sure this is not the very first one like this considering the vins matched same exact transmission to interchange.

Or is it possible to replace just the tail shaft to the transmission that has the tone ring in it for the VSS??