I updated /sass/site/primary/home/_hero.scss in the following way. This seems to be a reasonable compromise between being fold-focused and having a fixed aspect ratio (although there is a bit of an overhang at the bottom of the video at desktop size).
I also needed to add font-size: 0; to .heroVideo. This workaround makes no sense and shouldn't work, but as far as I can tell, it works, and it works across browsers.
.page-template-homepage { .site-main { .homeHero { … .heroImage, .heroVideo { … video { width: 100%; height: auto; } }