OK, here is the long story of how instant POP works...
On regular paper, contrast is fixed.
But POP works differently. It is a self masking process. Consider it like if the paper did dodge & burn itself automatically. This allows great control over the contrast range. Incredibly dense and contrasty negatives can be printed with normal contrast. That's why it was so used in the early days of photography.
The way it works technically is that the lighter parts of the negative make the image darken fast while the dark parts of the image keep recording detail. It's that simple. By controlling the amount of light that hits the paper, you can even out the contrast range.
Since this can produce a lower contrast image on grade 6 paper, it stands a better chance of providing a more even negative. By working differently than normal paper, I think it might be a solution. Besides, all it costs is one sheet of paper to get the idea and see if it could work.
Don't forget, the longer the exposure, the lower the contrast. And since it works by inspection, you can pull it whenever you feel ready.
As far as high contrast developers, there's only the lithprint process (using litho developer) that could yield higher contrast.