I just went throught the SAME exact thing.
Mine was surging a bit at idle. Not too bad but enough to notice. and would die EXCATLY the way you describe. TVS2300 and all.
Only difference is mine would start faster than that.
Turned out to be a header gasket leak. I used the felt Borla gaskets.
After that I agree with the fuel system. Check the gaskets frist though.