Depending on whether some of those people are small kids, you might be able to squeeze 6 on the rental carts at the Fort. We did...three kids in back and the little one on my wife's lap in front, with me driving.
I haven't seen any Disney 6-person carts personally - not sure if they have them. I don't think they frown on them though. Pretty much as long as it's actually a GOLF CART (and not a mule or other work-type or recreational vehicle) they should be fine.
I think the company we rented our 4 person off site from has some 6 person available... Golf Cart Enterprises http://www.golfcartenterprises.com/
PS - as for parking...
Shouldn't be 'problem' parking a 6 person, you just might have to look a little harder for a big enough spot.
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