Falker, I headed to Quantico last Summer in a position very similar to your own. Being 6'4, 215 lbs, running had never been my strong point. My 2 month pre-ship run time was somewhere around 25 minutes, and my overall PFT score was salvaged only by good pullup and crunches... I was also prone to getting shin splints, and had to structure my workout program accordingly. What I ended up doing was alternating daily workouts with running and some type of cross-training. Monday I would run 5-7 miles, Tuesday I'd bike, Wednesday intervals, Thursday swim, etc, etc. This got my cardio level up pretty quick and allowed me to leave somewhere around 23 minutes. Don't do the same run every day... throw in some hill runs, beach (sand) runs, and mix up the distances. Running the same route day in-day out will make you hate it even more. OCS does wonders for your running ability, as you will see. You'll probably realize before you leave that its in many ways more mental than physical. Over the course of three miles, a minute is only 20 seconds per... think of it that way, and push through. It is worth it, despite the obvious suck factor. Who knows, you may end up like I did and start to enjoy it. Good luck with the prepping.
OCS does wonders for both the mental and physical aspect... I dropped 3 more minutes, and saw some guys report running 25 that graduated at 19...