Leonard-– I am no expert on amino acids, and have no real opinion on glutamine. I do not know of any effect glutamine would have on insulin secretion. I know that glutamine is an energy source for the muscles, that it is found in protein (as are all amino acids, I believe), that meat and eggs are good sources of glutamine.
I think it is a very good idea to remove sugar from your diet!
Without glucose in the bloodstream, I understand that the body will automatically change to ketones as the energy source. It is not necessary to increase your fat consumption to effect the change.
However, medium chain fats, such as coconut oil, are very good for a person (even though coconut oil is a saturated fat).