I can only dream if it was that easy
All the instructions written to the drives firmware are unique to the platter structure during creation, including alignment ( on most drives alignment is key) So moving the platters around is instant death to the data. Plus in the long term of things it would be easier to just replace the head stack since the head stack will 99% have to come out anyways to remove the platters.
You never need to remove the platters on a hard drive unless you are dealing with motor issues or they need to be cleaned due to scratches, water, or fire damage.
So if the drive spins to speed which it is since you read the other surfaces, do not unscrew the platters.
as previously said before, this is data recovery 101.
just out of curiosity what is the brand and model of the hard drive?