My grandfather has a P-51 that he built it about 15 years ago. Last year he decided to finish it and we started flying it.  The plane has a Brodak 40 in it with a not so good motor run.

When the engine is running on the ground, and it gets up to operating temperature, it will start to detonate, surge, go slobbering rich, and almost shuts off. We have tried a different Brodak 40, and got similar results. We've changed props, spinners, fuel lines, fuel tanks and it still does it.  We beefed up the nose of the Mustang thinking that it may not have been built correctly all those years ago, and it hasn't helped the motor run.

When we started flying it last year, there wasn't any issue with the motor run and the plane flew right off the board. When we were running it in a 2 cycle last year, it was fine. But now, even at a 2 cycle, the motor will still surge but not as dramatic as when it goes into a 4 cycle.

Does anybody have any ideas what might be causing this issue with the motor run?

Matt,
its hard as you know to diagnose these kind of things, but judging from the fact that you have replaced all the significant fuel system parts, and the engine, I would suspect that perhaps there is a structural reason or a prop balance issue. Did you try a different  spinner? Fuel? plug heat range?
aside from that I would look at the area next to the wing, and the motor mounts to see if perhaps there is something loosing its grip on the wood structure.
It could be a heating issue I suppose, did you fly it in the same weather conditions last year? if so then I kind of doubt its heat related unless you are using different fuel.

HI Matt,

Not sure what to say except a "vibrating a lot" nose usually leads to lean runs due to fuel foaming. 

You say it goes slobbering rich........ not an indication of a flimsy nose in my experience.

Best of luck sorting it out.
Big Bear

     Matt, you can bench test for fuel foaming with a separate tank, off the airplane.  Helper #1 holds the airplane, helper #2 holds the tank and you start and needle the engine.  If this stabilizes the run, then start by adding two drops of armor all to a gallon of fuel.  If that doesn't resolve matters, than you have to disassemble the front end and inspect carefully for cracks, loose fasteners or bad joints/broken structural parts.  Flex and twist the fuse to try and get the cracks to open up.  Use good light and take your time.  If you can find the source of the vibration, dry it with K2R or talc and then epoxy/fiberglass it back together.  Unless something else came loose, I don't think resonance in the controls is likely the culprit, because the airplane worked right when it was first put in service.  You might have to look it over any number of times to find the problem.  Best, Tom