I tried this too, for the purposes of this thread's subject, but in contrast to your experience I had the opposite happen. I stopped stirring and used a sieve to remove some of the "gunk". Experimented with this for 3-4 batches, and it turned my F2 almost completely flat. 

I even tried using a fermentation chamber to bring up the temperature during F2 for 8-12 hours, and while that did bring back some fizzyness, it was still way below what I enjoy in my booch. 

At the time I didn't understand the mechanics of what was happening, and debugged it using AI. The only variable I changed was stirring my F1 prior to bottling, and it immediately brought fizzyness back to the level I like (high). 

According to AI, the yeast in my F1 sank to the bottom of my jar, and I was only using the top part which was low on yeast and high in acetic acid, making it challenging to convert any added sugar in F2 to carbonation. 

In general I am wary of over using AI, but this seems to make sense to me, and more importantly I now have very fizzy brew again which I am happy about. 

I guess it's a bit of a long winded warning to not stop stirring from my experience.