Hi.
I have EXACTLY the same problem. Engine idles high for about 20 seconds then dies. Mine has brand new piston, ring and crank seals, so it can't be compression or a crankcase air leak.
It feels to me as if it is wanting more fuel right at the bottom, but with the crappy SHA carb, you have limited adjustment. I will try replaceing the "Jet" for a larger one this weekend and see what effect it has.
Failing that, I have a TY50 carb somewhere which might go on and allow me to adjust the circuits individually.
One thing I have learned is that the small drilling which feeds the base of the "emulsion tube" with air is easily blocked, and can't be blown out. As much as I hated to, I ended up poking a bit of wire into it to clear.
Watch this space.
Peter