I definitely think a mixture is the way to go here.
Have your set meet and greets which will keep the planners happy, but sprinkle in a mixture of characters that randomly appear accross the parks.
Here's the thing, it does need to be RANDOM. With the Internet and social media these days, if a character is regularly meeting in a set location, you will soon get those who are in the know, and go there and look or wait for said character.
Once this happens it's bound to fail as two things will happen, firstly uncontrolled crowding of inappropriate areas (think Characterplooza). Secondly, guests who are dissatisfied when the character they are expecting to meet does not appear.
This can be avoided entirely if guests don't know where these characters will be appearing until it happens.