@blue_murr4
I think your goals are realistic. Max for females in the 17-21 age group is 42 push-ups, 78 sit-ups, and 15:36 mins for the 2-mile run.
First, calculate your BMI. Hopefully, it's between 18.5 and 24.9. If it's 25 or higher, then you need to lose a bit of weight. You'd be surprised at how much faster you can run and how many more push-ups you can do when you don't have to move around unnecessary weight. Having a "gut" will hamper your ability to get the most sit-ups. Caveat to weigh loss: you must do it
safely -only 1-2 lbs/week. You have 8 weeks until your APFT. You can lose 8-16 pounds in that time. Another caveat: sometimes, our bodies have a set point. Your weight loss may plateau even though you're doing the right things. Your body probably just likes a certain weight. Not much you can do about that. No fad diets to lose weight. Again, a safe and healthy weight loss plan (if needed) is how you should lose 1-2 lbs/week.
As stated earlier, you must include speed training into your work-outs. You can't improve your 2-mile run time just by running lots of miles. You need to work on speed in addition to endurance.
Integrate your work-out plan with that of your AROTC unit. In general, units have PT on MWF. Take a look at their training plan so you can adjust the work-outs you do on your own to complement the unit PT plan. For example, if the unit has a long run planned for Monday, then you may want to plan a speed work-out on Tuesday for your own work-out. If the unit has only 1 long run planned for the week, you may want to plan a long run on your own on Saturday or Sunday. If the unit has a regimen to improve push-ups on Monday, then you may not want to work too hard on push-ups the previous day.
For push-ups, you should shoot for a goal of doing 25 without stopping. Make sure they're good too. Here's a strategy I use to max the push-ups every time I take the APFT. Let's say my max is 73. I do 50 good ones without stopping. It'll take about 60 seconds to do 50 good ones. That means I have 60 seconds to knock out another 23. After doing 50, I rest (bow or arch back), do 5, rest, do 3, rest, do 3, rest, do 3, rest, do 2, rest, do 2, rest, do 2, rest, do 1, rest, do 1, rest, do 1. You can't rest a long time though. Just enough to arch (or bow) your back and move your hands in (or out) a bit.
So for you, do 25 without stopping. Let's say it takes 45 seconds to do 25 good ones (I don't know. You'll have to time yourself). That means you'll have 75 seconds to do only 17 more to max. So 25 good push-ups, rest, do 5, rest, do 3, rest, do 3, rest, do 2, rest, do 1, rest, do 1, rest, do 1, etc... Remember, each time your rest, you must go back to the ready position before you do another push-up.
Every time you walk into your dorm room, get on your face and crank out 20 push-ups (or whatever you can do without stopping). In time, you'll see the reps you do without stopping will increase.
Good luck!
Some of the Stew Smith resources can be found here. 
