To be fair Kingmaker was not an adventure where your players made the action. Any exploration of the area provided you with several side quests to pursue. More of then than not I felt somewhat overwhelmed by the sheer number of pressing tasks to be undertaken. It was almost like being at work. I have begun to feel my problem was not the number of quest all needing attention but how they presented themselves. There was a series of event that were scripted into the module which happened one after another. So there was always something going on and often requiring attention. I have actually tracked down a copy of the module now that we completed it to check out how it was suggested to be run and I can verify, the events flow in a series. You have a Lycanthrop problem, a rauble rouser, a cult pop which is followed by some trolls. Finally an owlbear rampages through the town. There are no triggers just one after each other.
This constant stream was a problem for me as we seemed to half ass our way through each. Nothing was given real attention as we were always considering something else and then being drawn back to deal with the problem in town. I think in many ways the sandbox nature of the game worked against itself with regard to the plot here. While the game includes rules for kingdom building, they were not tied into when plot elements were triggered. It was rather strange that grigory was causing problem in a town with a houses a blacksmith and a castle. If we actually had a town this would have been more meaningful. Also our city only had three completed squares when the owlbear hit, by the roles all of which should have been destroyed but the gm messed in reading and decided we only had two squares leveled. By the rules this could have easily totally destroyed our only city.
For me this was a huge missed mistake we should have had our city going to have meaningful gaming with these plot points. Even the werewolf made little since when the town had a small block of houses and a castle. We could just go to the few houses that were there and ask around, it wasn't a city it was more of a truck stop at that point and we didn't even serve split pee soup! My suggestion for game masters running this campaign would be to put a city point trigger on each of the main plot driving events. In dungeon crawls you roughly have level gating monsters and thing you can't handle from bulldozing the game. Here with the sand box that is thrown out the window, but you have this kingdom that is central to the plot of this and every future module in the adventure path. A fluke destruction of the city can end your gaming session very quickly.
Really the problem is not player driven or plot driven adventure the problem is one of goals. In any game you are going to arrive at a set of in game goals and if they are generated via the player or game master it really doesn't matter. Distracting a player from a goal they are working at is generally bad. You have them engaged and having fun, why distract or hinder them. Also I have found being on the other side of the screen if I die to a random encounter I am pissed if I die working to achieve some goal I care about I have fun. Ask your players their goals and make note. Also work out the goals your adventure is asking the players to accomplish. Work on creating a timeline of those goals, do they have prerequisites if so make note. You may find you create a map of your adventure with pretty minimal work one tied with goals. You can next have those goals being the triggers for bigger events. Maybe the invasion force doesn't attack laketown until a fighting ship has been constructed. Maybe everything does go on hold while the party does get its first trip to resupply. The goal is to give your scripted events a chance to play out in a logical fashion that short changes neither you nor your party. And maybe there are events that occur with the trigger of the party being low on resources. Its not to resupply your character I suggest this but rather to create a series of dramatic situations that feel as you intend them to.