Sure it can be done, just keep at it, working on improving your pushup endurance. Not stopping is a big component in getting under allotted times. But if you are getting frustrated and are hitting a plateau, there is nothing wrong with modifying to help get over the hump. I did it with pull-ups because I suck at them. I was really struggling to even come close to L5, so I added a modification when I ran into trouble. There is no crime in doing that. I see you already modify your pull-ups, so do it with pushups as well. One idea is when you run into trouble, around rep 18 I see, go to your knees and lift your feet off the ground. It helps but you still get a nice workout. This will help condition your chest and arms a little more aerobically. You don't have to go to the next level if you don't want to, you could try this a few weeks until you can do 41 regular pushups in your allotted time, but this will help work on the speed of your pushups. That's just one idea. I'm sure there are others. But good luck and keep with it.