The NOAA Corps would be good for you, OP.
Their pilots fly in some of the most hazardous conditions possible. They're a uniformed service just like the Navy, but they do hurricane hunting and other hydrologic and weather-related research.
That's certainly a noncombat position and you'll be doing some good, and flying for a uniformed service. Win-win for the OP!
Don't the NOAA guys hold USNR commissions? Or am I sadly misinformed?
Oh and by the way, as someone who was educated by catholics (mainly Augustinians and Jesuits) I know plenty of religious men that have used "goddamn" to great effect.