I have experimented with this idea of trying to stay in ketosis through intermittent fasting, mostly through low-carb vegetarian eating with the addition of some fish. It works fairly well when your body gets used to it and subsequent fasting periods seem to get easier, at least for me.
The only thing is is that since you are reintroducing food, you do get some hunger back, but it tends to not be that bad as long as you don't start eating a lot of high-carb starchy unrefined or sugary foods. A small bit of challah would be OK, just not a loaf! LOL
The fasting doctor at fastingconnection.com talks about how when you start another fast within 10 days of your last fast, that your body has an easier time getting back into ketosis, and I have found this to be the case, especially if a moderate amount of exercise is added.
I have done numerous fasts and 2 fasts of about 21 days. Currently with my work schedule, I am not able to do that and have found intermittent fasting to be great, although the benefits are obviously not as great as a long fast, you are still doing a lot of great work for your body, particularly if you stick to eating "clean" on your non-fasting days.
If anything, you can try out your plan of fasting for 6 days and eating for one and see how your body reacts. Although you might want to try it for a while before deciding. It took my body a while to get used to IF.