I think your 6 year olds could probably fit in the front 'basket' but I don't know how they'd feel about actually doing it since many of the others who ride in those front baskets are Toddlers or Preschoolers. I think they could also sit on the seats in the middle between the people who are tall enough to pedal. I seem to remember the rental person telling me that my very tall 8 year old would be able to fit in the 'basket'.....I questioned that and she said that they've had adults sit in that basket.....someone who wanted to sit right up front because they were videotaping while on the ride! (I won't speculate on what led to that!)
Another option if your 6 year olds are really set on trying to pedal would be to check out the height restrictions for the surrey's at Old Key West. I don't know what they are there, but I do know that the minimum is lower because my ds was tall enough to pedal those when he was 7. I asked at the Boardwalk why the height restrictions were different than those at OKW and they said it was because they were two different rental agencies with different insurance restrictions. Boardwalk is fun from a total atmosphere standpoint, but OKW has an advantage of being flatter (doesn't have those two hills on the bridges which you realize are pretty big when you're in a surrey); also there are lots more choices on where to 'drive' the surrey at OKW.
Have a great trip!