When was the last time you went through the carb? If it has been some time it may be the diaphragm has finally worn out. Although that little hole in the cover doesn't pass much impact pressure it's possible it may now be enough to be a problem. There may be just enough pressure the diaphragm can no longer perform like a pump.

There may also be issues with the check valve flaps in the diaphgam on the other side of the carb. I'd replace them both for good measure.

The die off at idle sounds like fuel flow. Two places to go here. One is the carb screen. If it's loaded up with crud the engine will run very badly or die at low throttle positions. May get some missing or stuttering at higher throttle settings.

Next is a worn out set of reeds. They have the most impact at low RPM. At high RPM the crank rotation has more effect. Most reeds do not function at a rate equal to the RPM above a certain point. Unless they are ultra high performance stuff of course. Reeds rear out over time so a check of them once a year is not a bad thing to do. If creacked, chipped, or frayed at the corners, replace them. If they fail to lay flat on the cage either flip them over or replace them. A little lift here or there is not a problem but if an entire petal doesn't seat, get another one.

Finally, 3w had a bit of a problem with warping carb isolators for a period of time. They went to an aluminum version to correct leakage. If you have a plastic one, remove it and re-surface it flat by laying a sheet of 220 wet or dry on a very flat surface. Like glass. Lay the insualtor of the paper and slide back and forth, both sides, then check the finished surface with a known quality straight edge.