[racket] Functional struct update with subtypes

I played around briefly with define-local-member-name but it seemed
like a rather awkward way to achieve "protected"-ness.  From the
example in the help desk, it seems like the classes need to have some
sort of let wrapped around them to share a non-public method between
them.  It seems like to set things up so that each class shares fields
and methods with subclasses but no outsiders would be quite unwieldy
with many levels of wrapping and scopes that match the inheritance
hierarchy, which would be hard to read and hard to keep track of.  Is
it cleaner than I realize to achieve this?