A lot of this is familiar to me too. (And I agree that thin doesn't equal healthy.)
One thing I use a lot is from Michael Pollan's "Food Rules." (Which I do recommend highly, not sure if he'd find it interesting though.)
Are you hungry enough to eat an apple?
If no, you're not hungry. (If yes, go ahead and have an apple -- start there.)
We've also talked about allowing time to digest -- E.G. is a really horrible example there, he scarfs his vast quantities of food super-fast. When sozlet asks for seconds right after finishing, we tell her to wait a bit and digest, let her stomach catch up to her brain. (You don't feel full until a while after you actually are full.)
We usually have salad with meals, if she maintains she's still starving she can work on her salad for a bit and then if she's hungry after 5-10 minutes, she can have more of the main dish (pasta or whatever).
The nausea thing is actually really useful (never thought I'd say that), that's definitely helped. For example: A couple of weeks ago, she went with a friend to a local fair, just the two of them (no grown-up chaperones). She had money for dinner +, I trusted her to use it as she saw fit. She had a hamburger, funnel cake, something else (chips?), Sprite, and a bottle of water. On a scorchingly hot day.
The friend came over for a sleepover after the fair, sozlet barfed about half an hour after they went to sleep. (Friend slept through it, thankfully.)
Then she was fine, but it was a pretty clear cause and effect.
The next week she went to camp, where she could buy as many milkshakes as she wanted, and the food was generally on the unhealthy side, and it was scorchingly hot the whole damn time. (Like, over 105, heat warning, stay inside if possible hot.) She asked for a banana with every meal, had copious amounts of water, one milkshake the whole time, no soda, and had no problems whatsoever. LOVED camp. (Whew.)
Anyway, that's a digression.
In what way would Mo win the bet?