I looked at a rake this weekend. The tines are attached to the crossmember with one bolt each, like yours. Then, about 4" down the tines, there is a strip of metal - estimate about 1/2" wide - running above, and another below, the tines, from one end to the other, parallel to the cross member. In between the tines (which were not drilled), the strips were drilled and bolted togther, acting like a clamp on each tine to stabilize them and keep them from rotating.
My guess is that it's a lot easier to drill the strips than to drill the tines (thinner material and could be carried to a drill press), and possibly that lighter grade nuts and bolts can be used. The whole purpose of the clamping strips is to prevent sideways movement; there shouldn't be a lot of stress on them. I don't know how well it works, but I thought of you when I saw it. You could experiment with some scrap on a few of the tines.