What ratio of protein, carbs, and fat is best for losing weight?

All of them.

A caloric deficit is best.

I've lost 30 pounds in 12 weeks doing a 40-40-20 split, and I've lost 30 pounds in 12 weeks doing a high carb (300g per day) and low protein (only 90g per day) program. I've had clients lose on high, low, and everything in between.

Cycling carbs or going higher protein can certainly raise your metabolism - I did something similar with a client recently and raised his metabolism over 300 calories in a week and a half (in other words, according to the software tracking his progress, simply through shifting his macronutrients, we managed to allow him to eat 300 calories more to achieve the same results). The reason I did this was because his calories were so low, I wanted to raise his metabolism to give a better starting point.

The best solution for you is this - for the amount of weight you have to lose, it's going to take time. So you need a program you are comfortable with. Whichever program you enjoy the meals more and feel you can stick with most consistently, is the one you should go for. I have never had someone lose more than about 3 pounds of fat per week (if they lose more rapidly, the extra is typically water and/or muscle weight) but as far as those 3 pounds per week, I've done it successfully with cycling carbs, with higher protein, and with even high carb vegetarian diets, and it's always been more the total calories than the macronutrient breakdown that mattered.