1) It's monotonous in spots, with lots of areas without much going on
3) It's time-consuming, eating a lot of time that the more role-playing players could spend interacting with NPCs
Simple answer: Pre-roll/Pre-determine a lot of stuff--as much stuff as you can.
This way, you're exactly prepared for the upcoming scenario, and it moves smooth as glass.
In your game, you can quickly move them from point A to point B, all the time keeping the game fun and intersting.
However, hex-crawling does have the "sandbox" advantage -- namely, the players look at a map, they see a ravine, a swamp, a cave, what have you, and they say, "Ooh, let's see what's in there." and they go find out.
Another simple answer: Even in a sandbox, you, as the GM, can pre-plan and prepare a lot of stuff that you know is going to happen in the next game sessions.
Where the PCs have choice (they should always feel like they've got 100% choice), make up some quick contingency plans.
I usually set up some type of combat session as a contingency plan. Combat takes a lot of time, so I can eat up the rest of the game session with a contingency combat, buying myself time to develop the area the PCs want to go during the next game session.
I've got a game happening tomorrow. I expect to spend the entire session inside the dungeon, but there's nothing stopping the PCs from leaving the dungeon and going cross country at any moment.
My contingency plans are thus: If the PCs exit the cave and go North or West, they'll run into an enemy squad. Combat.
If they go east, they'll backtrack over land that they've already traveled. I've got a combat scenario for 'em
If the go west--same thing--I've a scenario that will buy me time to develop that direction.
I expect them to go south, so I've spent a little more time developing that way. Once I see which way the Players are going during our next game, the direction will get even more fleshed out.