The fact that it is running great up to the 3000 rpm mark is a bit odd.
Not if the problem is carb related
Is it starting first or second kick when both hot and cold, if so that rules out many of the common Magneto ailments and also the A/R unit.
rare possibility would be points spring earthing at higher revs, a longshot and depends on your points type/set up I think but Magnetos guys here will confirm or shoot down.
3000 revs? do you have a rev-counter fitted?, I'm wondering about this figure, would that be about half throttle, could be an air leak which does not manifest itself until sufficient suck in the manifold (higher revs), quick test - run a finger load of silicon around the carb inlet joint, let it set then go for a run.
Otherwise look at throttle slide, finger in the carb and see how much you can wiggle the slide about, also fuel supply to the carb, do plungers have two taps (sorry bit ignorant on plunger front) if so go for a ride with both taps on.
Just read dutch's comment, yes think that's along the same thinking as mine