There's a WWIII option involving China and, I don't know, some other countries (that obviously needs more research on my part, but you get the idea).
There's a rogue elements of the US Navy/attempted coup option.
If you [i]really want to[/i] Godzilla-abominations are possible, but I think human (or at least intelligent) opponents in naval vessels of their own would be much more fun.
I also prefer to keep this on Earth, rather than use teleportation-Bermuda Triangle shenanigans, but again, if you really want to, we can do that.

My favorite, though, is a business-as-usual scenario, with anti-piracy missions, maybe an encounter with some rogue Chinese forces (or something), military exercises against more conventional fleets to prove the worth of the program (and therefore your jobs), disaster relief first response, being deployed to assist an actual "professional" carrier battle group, "cooperation" with USSOCOM's mysterious orders (and being turned into glorified transport ships for said special forces, under strict orders not to interfere as things seem to go increasingly wrong with their mission [as best you can tell what their mission actually [i]is[/i]]), and blatant communication snafu's. I think a fun angle would be the contrast between JDF-1 and the conventional Navy and armed forces, with hilarity ensueing.

Though if you want to do crazy alien monster shenanigans, we can. It would likely mean more opportunites to fire your weapons. At least, more opportunites to fire them without getting in trouble.

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On another note, I like your sub, Wernher. The crew especially fills my heart with warmth and fuzziness.