Mostl RFSS accepted DSM34 training rifles for Allgeimeine SS units were Mauser according to contract. I have an image of an Erma DSM34. Comparing the RFSS marking, the Egun is a fake IMO. Notice the Sig Runen are not really runes. Rather the creator mated two slashing lines at the ends. And as noted above, the RFSS is marked on the opposite side of the butt-stock.
Here are a couple pics of my Mauser for comparison. These also only occur in certain serial number range but I don’t have a reference. The cartouche is different slightly.
It is on the correct side of the stock for Mauser. I think you are correct it is the wrong stock for that action. I haven’t been able to find any pictures with the cartouche oriented horizontally like that.