I've never had any trouble on my '65. I don't think either side should be that close to the edge of the windshield, to be able to "get stuck". I can see it happening if there's "slop" in the transmission linkages, or if they are "clocked" too far out. The springs inside the arms hold the blades against the glass, and stronger ones might make the problem worse.
I wonder if the motor is strong enough...mine's a reman single speed. Assuming you have 2-speed wipers, does the problem occur at different wiper speeds?