Have you learned about the safest ways to break a long-term fast?
I watched Fung talk about it once yes.
That's what I keep hearing. I guess I'm just not that motivated to do it yet.
You may aleady know this but from what I've learned, the reason you stop being hungry is primarily because your body switches fuel. It goes from burning carbs for fuel to burning fat and, as you say, your stomach "figures out" that it's regular dose of food isn't coming and so stops sending the hunger hormone signals to your brain.
Your body uses carbs, protein and fat for fuel when you're eating normally. But when you stop eating then yes you do transition to using fat stores for energy exclusively. That takes c. 24 hours but certainly by 36 hours you're cruising on all body fat by then.
When you're eating (unless it's 100% fat, like guzzling peanut oil I guess lol) your body's also secreting insulin (even protein triggers insulin secretion, not just carbs /sugar /starch), and when you're fasting now insulin's at bay. Insulin retains water among other things, so when you do fast you drop body weight quickly but a lot of it's water.
Once the water's gone from insulin levels dropping, your body weight reduces at a much more modest clip, closer to what you'd calculate your resting metabolic rate would consume (although unless you're laying in bed all day you're demanding more energy than just that).
I track my waist circumference with a tape measure, this doesn't show the volatility you see in body weight measurement, which as I said is influenced by water retention from dropping insulin levels. It's a more stable measure.