Ketone metabolism is not a 'rapid response mechanism'. Full keto-adaptation takes several weeks, and until that has been done, a slowly reducing level of ketones will spill into the urine. Once adapted, the ketones are barely present in the urine, having been used by the body (in place of glucose). (Resist the Monkey's meddlesome nature and accept that you need to learn new things all your life.)

It is rather childlike to concentrate on how often or when one poos. Perhaps it is due to your mum being anal-oriented during your early years, as a result you have too much of your attention focused on body functions which should follow their own natural schedule. My wife can set her clock by her toilet visit each morning, whereas I may go at any time, day or night, everyday or not, makes no sense, but just is the way it is, people differ in small details.

The carnivorous diet has no left-over rubbish and masses of dead bacteria to void and even if you wind up only going every other day or even less, it is of no consequence. Eating veggies like lettuce while attempting a meat diet will REALLY upset your gut.