I'm not sure how your engine could be "richening" on the initial climb out. The engine should be at WOT on climb out, so the regulator won't be having any effect, just the high speed needle valve. The HS needle sounds like it might be in too far, and so you might actually be lean on the high end, and that would be consistent with the hard starting problem as well. But if your regulator screw is out past flush, that would normally indicate a setting too rich, so I'll bet you've got some trash in the regulator, and you've had to richen the regulator some trying to compensate for it. Try cleaning it out, and while you're at it check the diaphragm and the gasket under the cover.

You might also check for an air leak on the pressure side of the regulator, the side where the check valve is located. If you're losing pressure there, it could cause you to lose your prime and force you to prime the carb with fuel before it will start. Check for pinholes, loose connections, etc. Good luck!

David