One other thing to look at that I have seen, especially after a restoration or change to a different engine in these antiques is a longer than normal loop in the fuel line either between the fuel tank and the gascolator, or between the gascolator and fuel tank. If this loop goes up a bit to where the top of the loop is higher than the level of the fuel in the fuel tank during an aggressive climb, the fuel flow will stop if you somehow get a bubble in the line (like a vapor bubble from a hot gascolator). Anyway, make sure your fuel lines don't run uphill higher than the bottom of the fuel tank in a nose up position then back down hill as that can create problems when your fuel levels are low. The last time I saw this was on a Taylorcraft that had been converted to a C-85. It had a big loop of line between the fuel tank and gascolator. Periodically, if the engine was hot, it would start and run just long enough to run all the fuel out of the carb and half of the fuel line, then would simply die and refuse to start again until it cooled down a bit. Sometimes that was during take off roll. The problem was addressed by simply lowering the top of the loop of fuel line. If I recall right, the J-4 only has an loop of fuel line from the gascolator to the carb, so check that it doesn't make a loop going up high enough to create a problem.

Hope you're having a blast with your J-4. It's a sweet airplane.

-Cub Builder