I just use a simple check-in. If two players are talking, or one player is taking a super long time, I’ll just politely turn to a third player (usually a quiet one) and say, “Mary, what is Athena up to?” And then so on.
If they’re safe enough then they can heal to full, in my games. Is the abandoned citadel safe? Have the goblins given up and moved on, or are they trying to find a way in? In the latter, I would probably use some sort of timer to find out . Or just say "ok the Gobos seem to have given up, we will review every hour (turns in hours now).
Sometimes I let players move off strict turn order, especially when in town or somewhere focused more on Social than danger/exploration. In these cases, I “monitor” it by asking players who have not spoken yet what their character reaction is or what they want to do.
Not heresy at all. I do that some in down moments too, and it can depend on the group. Some groups are way better at respecting more shy players. As long as everyone is getting a moment to shine, and one or two players aren’t running away with the show, it’s all good. It’s just that turn order and simple check-ins solve that problem.
This. The turn rule, as I understand it, is meant to combat both stagnation between fights, and to keep certain personality types from dominating the roleplay. If those aren’t issues at your table, then just keep playing like a big ol’ badass.