If it is running OK inverted with the fuel tank level low, it may be the vent system is not working as expected. If you flip the plane over inverted with a full tank, does fuel flow out of the vent? I normally run a loop in the fuel line so it goes up and back down under the plane for this. That might prevent a slight vacuum effect if the fuel is flowing out the vent line, which would affect the fuel pump.  Of course the simple thing may be the the tank or tubing is moving and getting pinched on you when you go inverted too. There can be a lot of Gee forces involved.

The other thought is to use dual vent lines like they do for control line planes. The vent on top has a tube exit out the bottom and the vent on the bottom has a tube exiting out the top. Thus if the plane is inverted the bottom vent is now the top vent, and vice versa.

You could use a "Uniflow" fuel tank setup too. This keeps the fuel flow more constant as the tank empties.