couple of thoughts here:
1-Grease the groove (GTG) works VERY well on strength endurance activities like the sit-ups and push-ups. Pavel wrote a good piece on this using the swing as the exercise but I think it illustrates the need to alter volume and intensity to keep making progress:
Now for your needs you might shoot for something like this:
Day-1-30% of max push-ups performed ass many times throughout the Day ass possible (GTG)
Day 2-40% GTG
day 3 off
day 4 50% GTG
Day 5 20% GTG
Day 6 30%
Day 7 Off
day 8 Off
Day 9 Test-start with new cycle using similar volume progressions.
You can build this back from the date from your PT test so you allow for a few days of tapering..perhaps as many as 3-4 on the push ups ans sit-ups.
For the runs I would Hit one day per week of 400m repeats with 4 min rest between efforts. Start off with 4 sessions the first time, build each week by adding one more round till you are at 8 rounds. On another day, perhaps several days ofter the 400's run the 3 miles AT BEST RACE pace. Try to simulate the conditions you will be running in...time of day, if it's on a track is it before or after the sit-up/push-up test. In essence make it as close to your event conditions as possible. This will take a little planning to make your training coincide with the run but it won't be that hard. Specificity pay very big dividends so use it to your advantage to optimize your results.
On another day try shooting for FAST 800M runs with 4 min rest between efforts. Run 2 one session, 3 the next session and alternate between those.
Week one might look like:
400m day-4rounds, 4min rest.
Few days later race pace 3 mile day.
Few days later 800m run, 4min rest 2 rnds.
400m, 5 rounds 4 min rest
few days later race pace 3 mile
few days later800m run, 4min rest 3 rounds
Let me know if that all makes sense.
Regarding the heavy lifts...I'd focus on your strength endurance efforts...you can maintain ALL of your strength with just a bit of training. Use something like a 8x3 or 10x 2 with 85-90% of your 1RM on a Squat or Deadlift, a press and a pull up movement (bent rows can work). These should be on separate days and you need to only hit each movement once per week. You will not loose any strength and it will allow all your recovery to go towards the PT standards you NEED to ace.
Let me know if that makes sense!