It is hard to think of the mathematics while simultaneously doing a video so here is the explanation. The stiffness of a beam varies according to the square of the depth. So making a beam twice as deep makes it 4 times as stiff. Conversely making it half as deep makes it 1/4 as stiff. OK, so lying it on its side makes it 1/4 as stiff but also twice as wide, so that restores us to 1/2 the original stiffness. Better but still not so good.
On reconsideration, I am now going to put the beams back upright and double their thickness to stop this tendency to want to fall or buckle onto their sides. I need to find a supplier of proper bolts to pull this off. Usually this isn't so important but this house is going to have a living roof which will make it heavy especially when it rains.