First of all, removing the fan shroud is far easier than removing the fan itself, then you can then see any scratches that will confirm beyond a doubt whether or not the noise is coming from the fan!
The crossmember goes on top of the frame.
Remove the shroud and check it for marks instead of going thru all the guesswork you have done so far. Correction of any mecanical problem is a process of elimination. If the shroud is not scratched up, that eliminates all issues of engine/trans alingment; then you can move on to the other possibilities mentioned here.
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