Detail matters.
In an attempt to keep this brief, I glossed over the fact MyFormView contains another view component. This is fine, but it happens to be a form, and it's rendering before `@using(Html.BeginUmbracoForm <MyApp.SecondaryFormController ...` is closed.
This results in a form within a form which is invalid HTML and just breaks things.
Refactoring so the form isn't rendered within another form fixes the issue.