The motivation of your post - the fact that fallback is not necessary with many proportional pools - is not new. I've said this already
here (Table B.1) and before that.
The reason it's unnecessary because when there are many pools, you never get to 43.5% - there will virtually always be a pool with less than that. So you don't need any of the "random threshold selection from the range [0.5, 1.5]" nonsense.
I had only seen organofcorti's simulation and had not seen your (unfinished) paper before. I knew there was a mathematical derivation. I am just better at programming than at probability theory.
In my simulation too, there is little to no time spent at the backup pool when hopping multiple pools. For six pools however I found that there is still some time spent at pools being at > 0.43 (
see this post).