Well, you posted (2) tunes and no logs. But I will post up my msq which goes into idle 99,9% of the time, and is barely noticeable when it does miss. I will give some hints below, and then you can see what I have. I'm not saying it's perfect, but the delays and values that relate to your issue, fixed that issue for me.
1) After fully warmed up, with idle valve closed (if you don't know how to make that happen, then you are at square zero), and adjust the screw on the throttle body until idle is 100 RPM below your target. This should prevent stalls.
Oh, 0) establish and set your min and max control PWM's.
2) I use target idle PWM, not remember last one. These numbers are not just targets. The dashpot gets added to these, so they are important. These numbers, plus dashpot, plus fan adder (when fan is on), plus A/C adder (when A/C is on) all set the idle valve so that RPM's settle above your target RPM, then Closed Loop has a chance to take control.
3) Use a delay before going into CL, else you will sometimes go into CL at a high RPM and then the PID will drive the valve closed.