Gareth,

A simple try would be to run it richer than normal and see.

If you want to know what a pump could do to improve the problem of your engine, install it in a test stand with the biggest tank that you have, or with several small tanks connected in paralell.
Make it work for some time in those conditions and see how it does.

More volume of fuel will keep the level about the same for longer time; hence the pressure of the fuel at the spray bar of the carburetor will be as constant as with a fuel pump.

Best luck!