If a user is a moderator, they never see the solved_did_it_tho_title banner to prompt them to mark a post as the solution, and also don't see the prominent "mark as solution" button. This means we don't know it exists until a member complains about it.

This is because you condition both on $topic->isNotModeratorButCanSolve(), when it should really be something like $topic->isNotModeratorButCanSolve() || $topic->starter == \IPS\Member::loggedIn().

As feedback, I would like to be able to configure which forums the banner shows up in, and users get corresponding re-engagement emails - I have solutions turned on for all forums, because it is sometimes useful, but there are only a few where I truly want to push it.

This is currently intended. The banner and button is for non-staff members. If you would like to see this changed, please leave your suggestion in our Feature Suggestion forum.