What type stock for a 1927 arsenal rebuild?

[2AD_Vet]

I have a 1918 SA1903 that appears to have been rebuilt in 1927 (due to the SA 1927 barrel date.)

The finger-groove stock that is currently on it is in okay shape, and I don't want to ruin it further while shooting it at the range, so I was considering replacing the stock with something else that would still be appropriate to the rifle - preferably one with a pistol grip if they were used in 1927.

What would be the correct type/series stock used in 1927 on a WW1 rebuild, and would it have any particular inspection or rebuild stamps on it?

My current stock is marked "S" on the tip, and has JSA and then above it RA-P on the stock, but I don't think it is original to the weapon.

Thanks!

My current stock:

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