Not sure it's that of an issue but it's been a long time since I worked in this space. I can imagine a higher rate of spin with maybe a (large enough) circular plate underneath the square wafer would do the trick.

Spin coat as a circle then cut out a rectangle perhaps? I have no idea where the costs end up

At this point just keep going with circle wafers.

When you care about nanometers of thickness variation the gap always matters.