It does not appear to be consistent with any of the three styles of the New Model F listed in the Hunter Arms Co. catalogs of the period. The least expensive style at $20 had fluid-steel (Royal) barrels; the most expensive at $25 had basic two-rod Damascus-steel barrels; all had straight-grained wood.
I suspect that this is a special order gun. I would appreciate any insight on this. Also, if anyone has a similar gun, please consider contacting me to discuss at 703-625-4830.