I don't think ATF would go for it.
The Model 1707 was a short squat mortar tube that sat upon a tripod.
The Stokes is a long tube that sits on a base on the ground. The long tube has legs to hold the tube upright. The mount that attaches the legs to the tube controls elevation and windage.
The trick is to convince ATF that the two are the same.
What you might do is contact
Polemological museum of Artillery,
Engineers' and Signal corps and see if they can provide you with pictures or drawing of the 1707. Use them with your drawings of the mortar you intend to build and send the whole works to ATF for determination and approval. When you get the determination letter from ATF then post it here for all to see.
For right now absence any letter from ATF any mortar that utilizes the Stokes design or parts does not meet the criteria for posting on this forum. If somebody comes up with a letter from ATF saying stokes meets the antique replica description then we will hold the door wide open for these mortars on this board.