I do have an idea, but it depends on how far you are willing to go with rapid weight gain.
But first, the Live-Stream problem.
I thought about something like a canister for viewer interactions that you can buy or unlock (just like the Hose feeding) for the Streams.
Hose feeding will no longer be available in stream but the Canister will replace that function.
You can fill that canister with one shake or one Concentrate (with consent of course), which will hold for the whole timeslot. You have to refill every timeslot.
Now you can either manual start a pumpsession (1/4 of a timeslot) or make it viewer donation driven. Meaning viewers can donate to start the pump for a certain period of the time dependend of amount paid.
That way you can limit the GOAT shake to not be overpowered in stream but level it with the Concentrate.
Logically if you use the canister contraption, the streamer can no longer eat snacks or donated meals, since there is a constant pipe in her mouth, but still engage chat and fondle her belly.
Now to further spice it up, you could also add a donation cap value, which determines how much liquid can be pumped before the canister is empty.
For example let's say 400$. This means 1 manual pump has equal worth to 100$ (no spending if the girl belongs to you). Now if the chat donates so much that it exceeds the 400$, the canister empties which gives you the ability to refill it and fit 2 or more shakes in one timeslot.
It's all just an idea, so you are free to choose to implement something like this or not. First the canister itself and second the donation goal.
Imo the donation goalwould actually boost the engagment with the Live-Stream mechanic and also reward late game players with multiple shakes feeding.
Now back to the Concentrate. Let's say for now we keep the function as it is. Meaning it has a fail check and random reactions for rapid weight gain (the 350k cap you spoke of earlier).
Now...let's make it the GOAT again.
How about, we add a secret questline to the game?
The Obesity Research doesn't actually produce any results with their research, they just reward you with points that you can spend.
But what would happen, if they stumble upon the Concentrate?
Let's say they are oblivious to the Concentrate and don't know it exist. They only know that Dizzy Donuts are addicting.
Now if you would fatten up the researcher to the point of immobility and have them transferred to the Care Center, you are now able to hosefeed the concentrate. If you do, it will trigger the questline.
What the questline entails, I don't know. But in the end you will get an extremly valuable item that you can buy at Research (like 200 points).
This item will get the same treatment as the Mintleaf in "Monty Python's The Meaning of life". Not the bursting of course but the reaction.
So to trigger the Special Concentrate reaction you have to feed in one day, a snack or shake with the special Item in it and finish it off with the Concentrate feeding. If you succeed you get the Special reaction where all the calories gained that day will get multiplied.
Basically ballooning taken literally. Doesn't even need to be a 2x multiplier, since that could get crazy.
That way the Concentrate get's back it's place as the GOAT item.
But if you want to implement something like this, depends as I said on your stand of rapid weight gain.
And those are all just ideas ;)