The date limit for event cards are almost always near the end of the month.
In any case, you only need to start them just before the date limit (I mean they do not have to be done by that time). That is what I remember anyhow (you can test it once).
So here is how I played with Kingdom Management full on (Core) :
- Set my companions/counselors on missions of course ;
- check the date limits for the events I do not want to fail or ignore ;
- leave to adventure ! I rested as little as I could, really stretching thin my party, and attempted to be back to my capital before the date limits.
Sometimes, an event or two might fall between the cracks and not get done. It is almost impossible to do them all without fault.
Just before sending a batch of counselors on mission, generally near the end of the month, was often a good time also to have the hero/king do a two-week mission, that is those few cards where your character does nothing else for two weeks (those were the part of the Kingdom Management I did not like).
If you are careful, you will have plenty of time left to finish the last quest with success. You can attempt to get all your Kingdom stats to 10 (just for the challenge/Achievement: it is not a requirement), but it might not be possible: depends on when you want to do the last quest (avoiding spoilers here).
Nb: As I almost did not rest at all (to an extreme, beyond Fatigue), I could get a lot of stuff done in a week or so of walking around.