The star marking L looks like engraved, certainly not same as seen on period police bayonets, Richard You should compare it with Your other ACS police bayonets spine proofs.
The white frog have cracking by date area because of the area is moving on belt,this is a rivet line, the area where is the DH is behind the belt so it should be not cracked in no way. I believe Joe is right on this. The DH was there stamped much later. You didnt answer why there is a DH on LAH equipment?
To other piece the frog on 41ddl marked with additional DH and 41, i am not expert on this area on frogs, but maybe FP could help, one well known frog collector of Germany, is member here too, mentioned a short middle stitching frog were delivered only to one branch of Army.
Same as You have other army pieces here kvz 1943 not SS marked on a SS piece, why are the frogs, when there from beginn, not SS marked?