I have been thinking about ways of explaining things.
If Thompson does the smart thing and get a few good nights of sleep, a few options open up. The story calls for emotional and oratory explanations about why people should believe in shipgirls? Sure. Go for that. But be a troll about it. Storytime... and at the end a cup of coffee floats in for Thompson but isn't noticed before it is being placed on his desk, making people go 'waitasecond', but not being certain enough to actually say something.
Use stories about what people have seen other places. Use histories from bygone ages. Then use the hard facts to stop dead the counterarguments. When people instory inevitably go 'why did you not start with the hard facts'? The answer is: "I needed you to be in the right frame of mind, to avoid freaking you out more than neccessary."
Some troublesome scenes do almost beg to happen, of course... for example:
A couple of sailors swapping ghost stories while paining the hull - then going 'waitasecond' when they see the chief engineer come back from onshore a bit wasted, collapsing on the gangway, with seemingly nobody around, then the chief engineer, still unconcious, looks like someone picks him up and carries him onto the ship in the direction of the officers cabins, except there is nothing and nobody there actually doing it... For best effect, make one of the guys watching from hiding swear he thought he heard "What shall we do with the drunken sailor" being sung while this happened. If it was true or not would very much depend on what ship it happened on.