what about using the pulse of the crankcase for the fuel pump?
Brilliant idea! In fact it may be the only reasonably inexpensive way of doing it.
Suppose reed valves on one side of the crankcase [hopefully with a good air cleaner] could be fitted to allow 'one way' induction to the crankcase when the pulse was at negative pressure. Then another set of reeds on the other side and a pipe to the carb mounted on the Briggs engine. The whole carb would need to be in a box so that there was the same pressure on the outside as in the throat.
Really hard to say how well it would work based on the fact that the piston, after going down to compress the crankcase volume, then goes up a like amount. Might be possible to 'time' the opening of the reeds by opening and closing a port by the skirt of the piston.
When ya gonna start work on one!
At one time there were a few single cylinder 2-stroke racing bikes that had another 'pumper piston' connected to the crank. It was pure and simple a supercharger.