In my opinion, the basic geometry of the Tyler cart is ideal. For heavier loads I'd build a beefier frame/axle and use something on the order of a motorcycle wheel, it seems a narrow wheel spins more easily. The bracket that the timber actually rests on has 2 small "ears" that let you "hook" the timber as you lift it off one horse & rotate the cart in line. On the Tyler cart you can remove these brackets & use the steel saddles to move round material.
I'm thankful that there's not much in the way of oak timber in this part of the world, softwoods are heavy enough.