Re: ...Snyder board track style...
H.P. Snyder was one of the “Big Three” of the bike manufacturing world in the mid 30’s. They are best known for the bikes that were manufactured for and marketed by D.P. Harris as their house brand, Rollfast.
Between Harris and their many brands and Sears and Montgomery Ward, Snyder produced bikes with a variety of paint patterns and darts and diamond appeared on many. The star sprocket does feed the notion the bike may have originally been sold through Sears as an Elgin but it is possible that it was replaced at some time or that it was a pattern used on bikes branded for other retailers beyond Sears.
While the exact original branding of the frame may never be proven beyond at least a shadow of doubt, it is very likely a Snyder frame. Another thing to examine is the area where the main tubes meet the crank hanger. Snyder crank hangers typically have short, lug like rings that locate and reinforce the joints.
As for the original fork, A Moto-Balloon Snyder would use a Quadra-Plate fork with four flat plates (two are back-to-back so it looks like only three plates) and the early versions of the fork have heavy blades and a flat rather than domed top plate.