How about rigging a temporary fuel line from portable tank to carb. That would eliminate some parts. My outboard motor on my boat would just die on me at times, but when I pumped the primer bulb it would start and run fine. I borrowed a buddy's portable gas tank and gas line for a test. Outboard still died. I discovered the problem was the snap connection for the gas line at the motor. It was a bad part and resulted in a bad connection thus at times allowing air to be sucked in.
Also if the valve gap is too close then when the mower is shut off it temporarily heats up because it's not being air cooled. This closes the gap even more and effects the valve timing which can result in a loss of power when the mower is re-started.
Make sure the coil is good and the spark plugs are good ones with the proper gap. I had a Dixie Chopper once that ran fine down a grade but skipped going up the grade. That was a strange problem to diagnose. Found the coil wire insulation was rubbed off where the wire passed through the frame. Naturally the spark took the path of least resistance and intermittently grounded out when the mower was under strain going up hill.
I had a chain saw that would start fine but the instant I tried to cut with it it would bog down. I purchased the most expensive spark plug I could find and that solved my problem.
