You can try training and doing wide pushups instead. Dunno if they still allow it, when i was in the army a lot of people did wide pushups instead of normal cause it required less distance/energy to break the plank and get credit for the push up.
One member mentioned weight training, that's what i did to continually max my APFT. Don't rely on the daily morning exercises your unit conducts as most are poorly constructed and only provide maintenance if your already fit. Get a gym membership or use the free one on base and start weight train.
Other than that, gets lots of sleep and stretch for an hour the night before your APFT. Also make sure you have a good breathing rhythm for your pushups/situps.