ZenStrength

I would argue with recommending any kind of diet as an absolute one. E.g. keto. Keto definitely works well for people whose genetics is built for a fat-based diet, but that's not absolute at all, people who are born with a metabolism that promotes using carbohidrates as energy source would go very, very bad on keto. There are no absolute methods in nutrition. It should always be set specifically for one's genetics.

I must say that's an obsolete and not well considered criteria. When you do pushups in such frequency you rather rely on impact and the elastic capacity of your tendons than your muscle strength.

Intense interval cardio + metabolic weight training + a high protein low fat moderate carb diet.