You could go with the thicker board and...

A) Reduce the stringer height to compensate.
B) Cut the bottom of the top cap to compensate.

I would say if you tied to all four corners and to a center point you would be good as far as the top being lifted well. You might run into some issues with it wanting to tip and swing. Maybe tie something like a 2 x 4 across the two front and then another across the two rear cleats, then lift with those to make it want to be a little more stable.