That stock has been sanded badly, as well as finished glossy. That makes it tough to evaluate whether the serial in the barrel channel that also seems to be deeply struck is legit or reapplied. The font being used however looks correct. It would be easier if you could measure the diameter of the takedown disc. Sauer used 25mm diameter whereas all others used 30mm. Additionally your stock should have an Eagle 37 acceptance on the heel, maybe already gone due to sanding.
The serial of your rifle by the way is "5740s". This makes your rifle an extremely late one. Highest Sauer 1944 serial observed per Bruce and Steve is 230y. WaA280 on the receiver indicates production by Erma, what would be correct for the very early LSR sniper rifles. The first LSR sniper rifles appearing shortly afterwards, so I do think it is likely that this rifle was prepared for the LSR mount from factory, but finished as a service rifle and not someone messing around with it.
Since you had asked on your rear barrel band: you can simply pull it off, turn it 180 degrees, and reinstall it. Then you should have the serial atop and not on bottom. As it should be.
At worst you have a bolt and stock mismatch rifle with an original long side rail receiver action. At best you have a bolt mismatch long side rail receiver rifle. Both are very promising and you can be very happy with owning it. I wouldn't mind having one like this, so if you ever part with it, send me a PM.