I'm not a SEAL, but am Special Forces and was on a combat dive team. I would recommend focusing on building a cardio base to get your run times (and also weight down). Go easy on yourself with the running for now... avoid injuries. For example you could run two miles then follow up with 40-60 minutes on elliptical or stair climber. At least for combat dive school you have to swim 5k in open water in 90 minutes and run ten miles at a time... so building the capacity for long duration cardio is important (and you don't want to be exhausted when you finish). I would keep your long run at 4 or 5 miles and total weekly miles around 10 for now. Do most of your cardio low impact... as you get fitter and lighter you can increase the running, but do it gradually. Read ready to run by the supple leopard guy. Low intensity steady state is important, going balls out on everything is not good
I love being in the gym and tnation is awesome (I created a new account to reply to this, but I've been reading for the last 12 years and have spent over $10k on biotest products during that time). You need focus on your priorities now though. I've been doing a full body workout every third day (front squats, weighted pull-ups, incline bench, rows, push press, and deadlifts sometimes - and bis and tris of course) The rest of my training is cardio and calisthenics. I came from the opposite background as you, cross country runner etc, so I'm guessing you are probably stronger than I've ever been (I'm 5'11 and 190 on was on the bigger side of my ODA). I'd love to focus just on lifting, but being ready for the job comes first. I would try to maintain most of you strength with something along those lines (its about tradeoffs though, and you may loose some strength to get down to 7minute miles for distance)
So to summarize, I'd recommend full body strength every 2 or 3 days. You can do an easy cardio workout the same day. A longer run once a week, and one or two shorter runs (5 miles, 2 miles, 2 miles), then lots of moderate long duration cardio. Do sets of pushups throughout the day, you could start with 15 at a time, when that gets easy increase to 17, 20, 25, etc)
Also read "leadership and training for the fight" by paul howe. Don't let the statistics discourage you; a lot of things are within your control. Get comfortable in the water.
If you have more questions let me know... but this is what I'd recommend for a starting point. Please don't go on twenty mile runs with a cinderblock etc.
Edited to correct - 3km open water swim in 90 minutes