Your body generates glucose via gluconeogenesis on both high protein, and high fat diets. It generates it as a result of low glucose, as some tissues can only metabolize glucose. Glycerol from acylglycerides, as well as odd-numbered fatty acids can both precursor gluconeogenesis.

Blood sugar is also not the only thing that makes you feel hungry. The hunger mechanism is extraordinarily complicated, and still poorly understood. (For instance, low blood sugar triggers ghrelin release, which causes hunger directly). This sort of reductionist attitude that I frequently see applied to biology on HN is ineffective at best, harmful at worst. They are hundreds of more inputs and outputs to these processes, and what works for you is very unlikely to be for the reasons you think, and even more unlikely to work for others.

If these were simple problems, they'd be easily solved long ago.