I think you can do it. There are a few different variables to consider. Max strength which is the max amount of force your muscles can produce which is important because with a higher strength to weight ratio you use less energy. Which brings up two more variables, your weight and your muscular endurance. Loose unnescessary weight (body fat) and your using less energy on each
Pushup. Do this by training hard and
eating healthy, no need to
diet. Power is different than strength. Power is the rate at which you develop force. Power is what makes someone fast and explosive. If you draw a graph of Force vs Time you find out that the more power you can exert on each
Pushup, (in other words the faster you can reach the necessary force to push your self up) the less energy you use on each
Pushup. So power does not really increase endurance but it allows you to use less energy. Power is more a component of your nervous system. There are three things happenning that determine max power. 1)Max strength of muscle fiber which is determined by the cross sectional area of that fiber. 2) Neural coding which is how quickly the signal gets from your brain to your muscle fiber. 3) Motor recruitment - how many many motor units(muscle fibers) are being activated within a mortor pool. An intermediate athlete does not activate as many fibers simultaneously as an elite athlete does.
To train your nervous system you need consistency and repitition. you have to give your nervous system a reason to re-wire itself. Russian military did experiments with pull ups with phenomenal results. They put a pull up bar under a door way that the subjects would walk under at least 20 times a day. each time they walked under they had to perform 2 pullups. Do the same thing with pushups. 20 sets of 2-3 push ups every day. Remember this is training your nervous system and telling it that this is a movement you will be doing a lot of so it should become efficient at it. The point of this is not to tax your muscular system, or your nervous system for that matter - so it should not feel difficult. Next you need to be in the gym 6 times a week. Mon, Wed, Fri you are working the pushing motion. Heres the program:
Mon is endurance. 4 sets pushups max reps. 3 sets
ring pushups max reps. 2 sets of light dumbell press 30-40 reps.
Wed is weights. 4 sets of Bench press with weight you can do 12 reps. 3 sets dumbell press and 3 sets dumbell fly.
Fri is 4 sets Bench Press with a weight you can do for 3-4 reps. 3 sets incline BB press and 2 sets dumbell press All for 3-4 reps. If you have a heavy enough weight vest it would be superior to bench press.
Your rest interval is 2 minutes between sets for the first two weeks. Week 3 and 4 your rest interval will go down to 1.5 minutes.
Tues, Thur, Sat you need to follow this format with back or pulling movements. Examples are pull ups, Lat pull, Bent over row- barbell and dumbell. Look up agonist vs antagonist relationship of muscle for explanation. Also incorporate some core movements like plank into these
Workouts. Don't screw around with tricep isolation movements or machines, waste of time.
Do this program for 4 weeks, if you get weaker within that time it is to be expected. Week 5 and 6 you need to back off and let your body recover. You will use the same format of endurance days and strength days but you will not do more than 4 sets TOTAL in each
workout. this is important! This is when you get strong.4 minutes of rest between each set. It will feel super easy if you made it through the first month and that is the goal, its called active recovery.
EQUALLY important are rest and
diet. If you are going to put this much effort into the
Workouts match it with your
diet and sleep. Sleep 9 hours a night, this is when your nervous system recovers and re-wires itself. Most people put a huge emphasis on protein, but don't forget fruits and veggies, whole grains and nuts. You would be amazed what a pro body builder actually eats-lots of broccoli.
Good luck, and appologies if posts of this length are unwanted.