Those strips only 'work' (turn purple) if your body makes ketones( for fuel) and then lets them spill into your urine. If you are starving yourself your body is probably going to hang onto every bit of fuel it can, plus burn it more slowly if possible, any way it can (including not wasting any ketones through pee!).
Add to that, you may be metabolically challenged anyway (so am I) or rather, "fuel efficient" LOL and will never make extra ketones out of fat when you do burn it.
I do think you could stand to eat MORE (like, add some vegetables, and get your body thinking "I'm not starving") and drink more water...
Boot camp might be a good place to get things stirred up. BTW, you didn't GET fat eating 2 eggs and a shake a day, did you??