If the engine leans out when the nose is raised, then the difficulty is simply a lack of fuel pressure to the carb. Either the muffler's not delivering enough pressure, the fuel tank's too far from the engine, the fuel line's too small, there are leaks/kinks in the fuel line, or a fuel filler valve is leaking air.

One solution for larger engines is to re-plumb the fuel system with larger tubing. You'll have to wire-tie everything in place because the larger tubing doesn't grip the metal nipples as well as the smaller tubing. We also re-plumb the tank with larger tubing. Many tanks won't allow you to do this. Make sure you have one that does.

If the engine will run "all day" on a test stand with a good fuel system setup, then there's nothing wrong with the engine, and you have to start checking out the engine/airframe/fuel system combination.

[edit for typos]