You have to find out how many calories it takes for your body to heat up again - I’m sure there are estimates somewhere. My prior is that it is not that much, but am interested in finding out.
Burning off glycogen faster is a great idea. Most people do it by exercising. I have read that your liver stores ~400 kcal and the rest of your body around ~1600, so your body should start producing ketones after you spend around 2000 kcal without eating.
It’s an interesting idea, and while I don’t have the education and background to really know… My gut feeling is there won’t be a huge impact. Having said that, it certainly can’t hurt! Although I believe the advice you got regarding a low-carb pre-fast meal would be most effective, followed by exercise during your fasting period.