Not sure if I know 'more' about the process in terms of the science. I suspect the soap, a surfactant, transfers with the sap/enzymes and softens the cell walls as part of the process but pure conjecture.
I was taught to, and have always used, dishwashing soap. I think it is septic safe and therefore should be safe for other uses. I would NOT recommend laundry detergent (I'll tell you a story sometime). Still, soap is basically a surfactant that serves to make "water wetter". I mix 50-50 with water - which makes it pricey - a little less than $100 a trash can full. I use plastic trash cans so 20 gallons of mix. This mix was light on soap (gallon maybe) because I got tired of buying it. Buy the cheapest you can.
Three months is probalby 2X longer than I usually soak but I've been turning a lot of green wood this year. I have never considered the bowl wall thickness relevant for the soap process but haven't studied it.
In the past, when the soaked bowls were removed and dry to touch, I would put them in boxes/bags with wet shavings, weight them and track the weight loss. Probably harvest a 1-2" bowl in 6 months for final turning. Paper bags seem harder to come by now. Boxes, I'm too lazy to hunt, to cheap the buy. May have to touch up the diner down the road for used boxes.
Sometimes, I've weighted the bowls, not these. When I would walk by, on occasion, I would flip the top bowls that were sitting on top to keep their exposed sides wet.
I've got two more trash cans of green bowls 'soaking' in shavings, open lid. We'll see how those go.
FWIW, it is amazing (to me) the amount of sludge yielded from the soak.
Hope that helps.