Many years ago I passed up an ArgentineCarbine that had a bore so far off center at the muzzle that it was clearly visible, the crown had been turned on center. Near as I can figure the barrel was a replacement made from a cut down long rifle barrel. Mauser bores are known to wander a bit.
Since at one point it was found that perfect straightness of the last six inches of bore governed the rifles accuracy potential, and for a time at least straightening of bores was limited to the last six inches to speed wartime production, could this rebuilt No.5 have been fitted with a cutdown No.4 barrel?
That might explain why it would shoot so far to one side. If the original bore wandered a bit that is.
If cutdown No.4 barrels that weren't straightened full length were ever used that could contribute to Wandering Zero as the barrel heated up.