Sorry, but you're wrong about diabetes causing obesity, which I think was your initial argument. In fact I find that if a 'diabetes nutrition class' tries to convince you of something, it pays to check all the facts before you go much further. Many are simply repeating what they've been told and don't particularly appreciate an educated argument.
Initially you said that obesity caused diabetes, but then your later reply states that it was your diabetes that made you overweight. So which was it? The sort of hunger you describe is highly likely in many cases to be a result of a poor blood sugar profile, which probably indicates insulin resistance or type 2 diabetes (full-blown insulin resistance!)
We're not going to disagree that less body fat leads to less insulin resistance. But it's best not to resort to calorie counting in an attempt to shift the pounds. That's what leads people down the blind alley of a low-fat diet. A low-fat diet is not only fundamentally unnatural and unhealthy, but increases the amount of starch in the diet and as a result messes up your blood sugars further. The 'Fat diabetics' you describe have I think generally been badly advised and fallen victim to this phenomenon. Did your 'grand experiment' not lead you to the same conclusion? Surely a 'person who processes glucose incorrectly' is probably a person consuming too much glucose, resulting in weight gain and diabetes. And we ALL turn excess blood sugar into fat, not just diabetics. Our glucagon will not start to convert stored fat into glucose unless our insulin levels are sufficiently low - which they never are on a starchy diet.
Now I'm a slim (Type 1) diabetic, and I've had the condition for 26 years. But it wasn't till I abandoned the 'recommended' diet that I became slim and started using much less insulin. Since I eat a lot more fat than I did before, I'm certainly not on a low calorie diet but my lipids are great, blood pressure too, and my blood glucose levels are those of a non-diabetic. None of those things were true beforehand. In other words, my diabetes didn't make me fat, it was the way I dealt with it.
All the best,