Someone who lives or has a house on North Ambergris can answer you better, but I think I would like to have a golf cart there.
Belizean Shores if I recall is about as far north as you can easily go with a cart, but it would be handy for running to other points south of there and in going to town. Believe the fee for cart and passengers across the channel is now US$2.50 round-trip.
A few cart renters don't want you to take their carts north of the river.
--Lan Sluder