Rest more, let your body recover so you can do more volume the next time around.
For what it's worth.. in my OCS class there was a swimmer and he was running the PFT in like 16 minutes. I got home thinking I was all bad ass and went swimming based off of how much he said it would help, did like 2 laps in an O size pool and was dead. Probably because I have no technique and am aerodynamic as a brick in the water, but still. You sound like an ectomorph... you need to eat eat eat eat eat.
If you don't mind me asking; What is an ectomorph? lol. Was that 16 minutes for the 3 mile Marine PFT or the 1.5 mile Navy PFT?
I do my 72 laps in increments of 10 laps. 10 laps, rest 30 seconds, 10 laps, rest 30 seconds, etc... Sometimes I switch it up and do 8 laps, and 2 underwater with the same rest to increase my lung capacity.
Edit: I found it. http://www.muscleandstrength.com/articles/body-types-ectomorph-mesomorph-endomorph.html