> The standard rig produces a non-zero sideways moment that alternates between $-4Fr$ and $+4Fr$ during each stroke. The cox is going to have to work hard to counter that wiggle
I don't think so. Because the net force over a stroke is zero, the cox can just ignore it, and it will even out.
The other problem here is that your analysis is non-quantitative: to know whether this is worth worrying about, you'd need to know how large this moment is compared to the natural variation, stroke to stroke, that people produce anyway.