I think you still can't overcome 500 calories of deficit. If you ate pure protein you will still be in 150 calories of deficit using the most conservative numbers (30% overhead to process protein).
But this is assuming you calculate your daily calorie burn with one diet that is pure protein and then convert to one that has 100% calorie availability, you still can't overcome 500 calories of deficit on paper!
Realistically you would change diets, then find your baseline based on the new diet, and then calculate a calorie deficit from there. In that case you would be very close to a 500 calorie deficit, and you would unavoidably lose about 1lb of fat per week. A 500 calorie deficit sucks but you will adapt to it in a few months if you stick to it. I've managed to lose over 50lbs in the last year, probably close to 75lbs of fat mass. (I did use a GLP1, dieting is hard)