If it were me, I would contemplate dropping presses while training the pushups until you are able to reach the required reps easily.
I'd move the bench press to Wednesday and do single sets with a high percentage of your 1-5rm and put pushups on Monday and Friday, with 3-5 sets till failure.
Maybe implement this 4-6 weeks out from your PT test, and then resume normal programming afterward.
This may be taking it a bit to the extreme, but at least you will get really good at pushups .
-Hat