If you want to make sure you have zero issues when your testing time comes - just train really hard at them. Put your nose and entire chest right to the ground during every practice pushup and you won't ever have to worry about redoing one! If you can't go anymore - switch to girl pushups and once that's maxed out just use your arms and do mini girl pushups. It may sound sissy like to do those easy pushups but that's how you push your muscles to their limits. Personally, I'm in university now so what I do is open up my history textbook and every two pages read I get into pushup position until I can't go anymore using the above training methods. And I repeat sets of this for at least an hour, maybe two as you progress. Go until your arms are so sore that you have to use your elbows to roll yourself over to get back up. It kills but it works.
You'll find if you max out your muscles every second day doing pushups that every time you hit the floor you'll be able to do at least one or two more after every rest period (until a certain point) Pushups are hard work, especially if you have week triceps, I'd recommend swimming to build triceps. Swimming is also great for working on your shoulders which really helps pushups. The pulling motions of every stroke really works the triceps. I'm sure what you found was that your wrist or arms were giving out on you before your chest does. (That was my situation)
The angle you're supposed to use is the one that works every muscle in your upper body the most and by practicing push-up sets till you can't do anouther every second day will soon allow you to discover where that spot is.
P.s. I was sorta at the same spot a year ago. Could run like a madman, super leg strength but getting 15 pushups out of me was murder, lol.
My personal advice would be to make it so that even if you screw up on your first 20, you can do anouther 20 easy. My recruiter let me keep going and didn't say stop after 19. Some apparently tell you, good 19 and try to stop you. Just say you have more in you and leave an impression.
I looked at it this way, you have to do 50 in the US just to get in, so I better be able to match those punks
Just saying work your ass off at pushups on your own and you won't have to worry about chance and getting a more forgiving instructor. Good luck man - it's worth it.