The markings on both guns are indeed fake. Although the earlier gun (sn 733016) is a 1920 gun, it is possible it was assembled as a trench gun, but not under government contract. I know of two other 1920 trench guns. One is in the 744xxx serial number range. The second gun is in the 720xxx serial number range and was part of the Pugsley Collection owned by Winchester. It is now owned by a private collector. Neither of these trench guns were martially marked.
And keep in mind that there were commercial Model 1897 trench guns that were made for law enforcement between the WWI and WWII. Many of these are in the 800,000 range.