I have photos of two EP&S SA daggers. One Rohm and one not. Both have perfect dagger to scabbard fit. Yours appears have a substantial difference in curve. It could be the photo but if not, I would expect a perfect fit on a Rohm dagger.
Do you have pics of the SA inscription? Also, carefully compare the edges of the etches on the front and obverse for the same depth, background texture and edge detail under a loupe or USB microscope.
I believe your Rohm inscription to be a post-war enhancement, does not match the Pack style inscription which is quite specific to this maker. Unfortunately Pack Rohms are the well copied, Attwood did a decent copy of these back in the day, and are quite difficult to spot. Luckily with his Eickhorn repro blades, there were major design flaws, so easily detected...
Red Baron is 100% correct. Not the distinctive Pack inscription. So suspect a fraud. I trust that we will not assist the fraudsters with a correct Pack inscription example being posted here. Sad, but this is what it has come to.