914 Engine Nearly Quitting

Possibly vapor lock, but since it's new then I'd pop the carb bowls off and look for debris. More likely now since you're flushing fuel through a new system.

If you purchased your gas locally (Maine) in the last 90 days, you most assuredly have "Winter Gas" (RVP 14).
This gas will have vapor problems above 13,000 ft if the fuel temp reaches 70°F.
If it was a warmer day to start with, or a hangared plane, each time the fuel passes through the engine it is warmed slightly before being returned to the main tank via the Return fuel line.
Each pass warms it slightly and as the fuel volume gets smaller during the flight the effect gets greater.

An Aux fuel pump as close to the main tank as possible, and before the pressure drop of the gascolator, can help prevent this problem by keeping the pressure in the fuel lines above the fuel's vapor pressure.
This is especially true for a low wing aircraft (Sling 4) where the fuel flow is uphill all the way.