Yeah, I thought of that issue (pressure in the fuel-reservoir aka lighter), but I don't understand why this would only be a problem in my idea.The problem with your solution is that the dual piston mixing relies on the fuel being at atmospheric pressure, but it's stored at higher pressure in the reservoir.
Or would you let the fuel slowly drain out of the small pump-shaft (where I would have added a seal), to keep the fuel-pressure (before the compressing) in the pump cylinder at atmospheric? Sorry I'm a bit lost...
Edit:
When you start compressing the fuel in the pump-cylinder, the pressure there would be higher as the pressure in the fuel reservoir, and the check-valve would stop the flow.but there is nothing to block the flow of fuel to the chamber...
Or did I misunderstand you?