My understanding of your post also was, it might be that the No-God itself is just a tool to reduce the population to the blessed 144k, with no other function. Which would mean the 144k is what needs to be achieved, not the No-God. Personally, i don't think so, as I've outlined above. But that's in no way certain, and is mainly based on the fact that the existence of the No-God even without the world being reduced to the 144k has a certain effect on the great cycle of souls, which involves the Outside. Additionally, there is that whole "invisible to the Gods" thing.
Bakker said in a Q&A that when the Inchies inoculated the Nonmen and it resulted in the death of the females; that they then found a dread function for the No-God. I assume that means that no births will occur during the rise of the No-God.
I have seen theories upon theories about 144,000. It's the only reason I mentioned it. One, that during Akka's dream where Nayu is a wretch in line, being led to the Golden Room, that the Consult was feeding the No-God. And, once it had 144,000 souls it would rise. We now know that's patently false.
The Outside is not shut, correct. Bakker has even stated that the gods can function, as you've said. But, the No-God has stopped the cycle of souls, hence the still births. To shut the Outside, it would seem that the No-Gods purpose is to whittle the population down to 144,000. It's like a threshold needed to shut the Gods off from the Inside (Earwa).
Again, I never expect to get the how's of things, only the why's.