OK, I have everything fully researched. Now, none of the villagers want to research anymore, but there's one in particular I'm trying to get to be a Master Researcher, so I keep forcing him to research. It keeps saying "This villager improved at Research!" but his bar doesn't ever seem to move up. Can villagers accrue research skills once everything has been fully researched out?

Villagers can continue to research at the table and gain skill as scientists even after all levels of Village Tech have been purchased. The amount of increase in a villager's skill becomes less and less the closer they get to master. This is true not only for scientists, but the other skills, as well.