Vegetable or "tooling" tan cow hide at a 3~4 oz. is what I use, but as Beaverman says a heavier leather will work, its just more of a wrestling job to stitch and turn if reverse stitched...Also, most of my dying and antiquing techniques are especially geared to the "vegetable" tan leathers...I dont think many of those techniques would work on commercial chrome tans...which is what I suspect your moose leather is.
Dont give up on the moose splits...depending on what color they have been dyed, which can also be altered, they would make a good Native American styled pouch. And the softer split leather would lend itself to very well to quill or bead work...Use a "whip stitch instead of saddle stitching for construction, and you can apply creamed mink oil to the out side of the pouch to give it a greased, slicker and more used antiqued look. Dont incorporate fine leather fringing with the thin split leather, as the fringe will tend to tear...and if you think the leather is really too thin, simply line it with a light weight trade wool or even early styled cotton print...I have always made use of commercial garment suedes as a substitute for higher grade smoked brain tans in a pinch, and you may be happily surprised with the results you can acheive with your moose leather...besides, at this point you dont have anything to lose except a bit of thread.
Id consider any N/A styled bag from the early open top version seen in the famous "Death of Wolfe" painting,and common in the 17th anb 18th centuries; to later Seminole or Great Lakes styled bandolier bags...
T.C.Albert