HDD repair by transplanting platter into new drive of same model?

Paperdoc

Polypheme
Ambassador
Impossible. Unless you are a hard disk manufacturing factory that has fancy clean rooms and trained technicians.

The process you are talking about is delicate skilled work, But even if you could do it, it MUST be done in a special "clean room" with no dust. Any normal dust particle - and this surely includes all the microscopic dust you cannot see in the air - is larger than the tiny gap between a disk platter surface and the head that floats above in on a film of moving air. When that particle gets caught under a head, it starts to dig a deep gouge in the magnetic coating of the disk, thus destroying it. So you cannot do this kind of repair without a LOT of very special equipment.
 
It can be done.

Step 1: package the drive securely in a box.

Step 2: Ship it to a data recovery service. They will do exactly as you want in their clean room and performed by trained technicians.

Step 3: Write a large check to them.

Step 4: Hope that they can pull your data off the drive(it's not a guarantee).

Step 5: Begin a data backup plan because you never want to lose your data again due to a drive failure.