Yep. Put one on my .243 M71, long ago. (Had it black phosphated too.) It may well have been a 70A stock. A guy bought the rifle just for the action. I bought the stock from him for $20. Told you it was long ago. In any case, it went on with little fuss.
The recoil lug on the M70 is about 1/8" forward of where it is on the M71. No big deal. You just remove a bit of wood in the M70 stock's recoil lug slot and the whole thing drops right in. You will need to glass bed it or the recoil lug will not be touching anything. That's no big deal either. Get an Acraglas Kit.
The trigger guard on the M71 is a bit shorter than the M70's. I didn't have the M70 guard, but it should be fine. If not, just use the M71 guard. Mine just has the aft screw. It's never been a problem. The trigger sticks out 7/8" into the guard.
My barrel is floated. Glass bedding didn't make a lick of difference accuracy wise, but the rifle is very consistent. It's pretty as hell too.