It's possible that you can mark all of your messages read, turn on airplane mode (so no new messages come in), verify that there are no badges on icons, and then go into settings / apps, scroll to all, look for the app "Badger", tap it and force stop and then disable the app. I think that would keep the unread badges from showing up from that point forward (though I don't know for sure.)
Installing the Google Now launcher seems easier (though if you don't like the Google search bar, then, not so much; then, as was previously said, maybe Nova Launcher is a good choice, because that won't badge the icons and you can disable the Google search bar.)