NHK=plausible? I dunno. Sure, hikkis are an actual problem IRL over in Japan, but there's the whole delusional aspect.
For stuff similar to 5 cm/s, go for Shinkai's other major works. Well, they're mostly fantasy sci-fi (with stuff as outrageous as the multiverse and the "universe dreaming") but in the same romance vein. Shinkai's short "She and Her Cat" is kind of nice too, practically a solor work IIRC, and other than the Cat "talking," is completely normal.