Been fighting a fuel issue myself, about got it resolved. Biggest issue on mine was a HUGE vacuum leak, or multiple ones. I found both idle hoses leaking, at least three injector seals leaking, the injector body to intake boot folded over and leaking, my EHA was leaking and the O2 sensor was shot. After fixing all that and THEN adjusting the mixture, it seems to be vastly improved, but still tweaking.

Yours certailny sounds like an extreme lean run situation. I'd start by inspecting the idle air hoses, checking the EHA for leaks and consider a new O2 sensor. Might also check the idle microswitch. Whatever you have going on, it's fuel/mixture related, from the sound of it.

Big thing is to hit youtube and learn how all the components of the K Jet system work and inter-relate. It's not super mysterious, just totally different from any other modern EFI out there. Last time I dealt with one was in the early 80s on a 72 VW squareback.