Transmission crossmember should only fit on the car one way. The holes are not the same from side to side. However, over the years most anything could've happened to the parts you have. My car came with the wrong transmission mount and it took me a while to figure out the problem.

I have a CSR shield and it does not fit under the stock floor when the engine is in the location that TTi wants.

Do you have your headers yet? If you have your headers you should bolt them on the engine while you are at this stage. Depending on which headers you are using they can change everything. I had to start over once I tried to mount the headers. I had to move a bunch of stuff around and I still haven't quite recovered from that operation.