Sorry, I don't know if I'm the only one but I found this really confusing to follow and visualise. I understand if not, but is it possible to share the link so we can have a look?
Multiple H2s is fine and whether there may be an issue or not depends on how similar they are and how many exactly. Obviously 50 duplicate H2s will potentially be seen as spammy. As for the invisible text, is this hidden to users with something like display:none so is still readable by crawlers? If so, Google doesn't approve of hiding content or making content inaccessible to users with the intention of manipulating rankings. It may be seen as you deliberately attempting to get your keywords in for SEO, without it being of value to the user. With the perspective that if it it had value to the user, then it wouldn't be hidden. So it must only be there to game the search engines.