Hi there dangermouse
I haven't tried it as such - as I don't tend to do any of these diets with names but just follow general priniciples - although I have been on a pretty low carb diet. Mine was for weight loss and suggested by my son who is into muscle building and weights and thought I was eating too many carbs ( even though they were all healthy!). Any low-ish carb diet does have the fantastic benefit of regulating blood sugar levels as you have found which is recommended for those who suffer severe pms and any hormonal fluctuations because of the effects of oestrogen and progesterone on blood sugar metabolism - so I can imagine is also good for peri-menopause too. Not sure about it being an alternative to HRT when peri-menopause proper kicks in though, but a good start for feeling better and less dizzy/light-headed!
I presume what you can taste is the fruity taste of acetone which is excreted when ketones are broken down and I think is smelt on the breath of those fasting or some diabetics (uncontrolled?)?
I've never done it as extremely as that ie induced ketosis as I still ate pulses and beans, and some root veg - but apparently it can have some effect even if carb containing foods are not completely eliminated. Although I'm still pretty low carb I have gone back to eating more - specifically oats for breakfast as I have high cholesterol.
Glad you are feeling calmed as a result - I'm all for using diet to improve health and well-being
Hurdity x