To avoid a change in the "web" breaking something, you could put in checks like "at this point, the tangled code should equal this SHA in git" (or maybe even just "this content SHA").
This is sort of like octave checks in lilypond (the music typesetting system) where, when using relative pitches, you can at any time say "this note is supposed to be in the 4th octave so flag an error if it isn't".