Aeronca Champion pilot reported an engine malfunction during climb resulting in an off airport landing while attempting to return to the departure airport.

Narrative

Header tank vented fuel cap failed to vent causing negative pressure on tank. This led to fuel starvation. The incident presented as Carb Icing. Pulled Carb Heat; within the same few seconds I also confirmed the position of both wing tank fuel valves; by cycling them from off to on. Left wing (4.5 gal); Right wing (0 useable); Header (full; 13 gal).I continued to climb to try and get as much altitude below me while I was trouble shooting. Pulling carb heat seemed to resolve the issue; I confirmed power full power was being made by the engine. Returned to on course heading. Engine once again began reducing in power. Made the decision to return to ZZZ. Engine was making roughly 80% power. Turned base to final and engine completely stopped; roughly 1.5 miles from End of Runway XX at approximately 2;700 ft. MSL/ 1;500 ft. AGL. 25 kt. headwind depleted my available energy. I landed in the grass on airport property; 500 ft. short of the runway. Root Cause; the pro-seal used to seal the header tank inlet created a seal against the header tank fuel cap. Preventing the fuel cap from venting. When I cycled the right wing fuel tank; I induced more air into the system and got a false indication of engine performance. I would have made the runway if I'd had turned base abeam the numbers. I failed to account for the headwind at altitude.