SO, it really piqued my interest that you ate in the 500–700 calorie range there for awhile.
I have been running some self experiments with myself (yes I nerd out on this stuff) for awhile with something called the Fasting Mimicking Diet (FMD) I read about in a science journal in 2015.
The diet is normally used for 5 days at a time, maybe one month for a variety of health reasons (including a longer life), but it boosts weight loss significantly.
The FMD consists of a complicated macronutrient mix (protein/fats/carbs) but additionally requires the participant to stay under 725 calories.
During this process, you dip into fasting ketosis, basically, your body burns fat stores instead of glucose from food for energy. It is like fat-burning nirvana.
I have run self-experiments and I get into ketosis whether I stick to the macronutrient prescription from the study or not.
All that to say, I think you could have in ketosis for a pretty good grip there. Nice work! Thanks for the good read!