Success! I can now display eight independent mono channels to the user while internally representing that as four stereo channels. Before I was struggling with how to extract the underlying equations that VSL is using to turn gain/pan into left/right, but I decided to give up and just brute-force it. I made a giant table (csv):

  pan, gain, left, right
  ...
  34, 80, 0.783, 0.69
  34, 81, 0.793, 0.701
  34, 82, 0.804, 0.712
  34, 83, 0.815, 0.717
  34, 84, 0.821, 0.728
  34, 85, 0.832, 0.739
  34, 86, 0.842, 0.75
  34, 87, 0.853, 0.761
  34, 88, 0.859, 0.766
  34, 89, 0.87, 0.777

Then to implement to_left_right(gain, pan) and to_gain_pan(left, right) I just find the table row that best corresponds to the desired conditions and use that. So if I call to_gain_pan(left=0.83, right=0.74) it will probably identify the line 34, 85, 0.832, 0.739 as closest and so decide to set gain to 85% and pan to 34%.

It bothers me a little to use something so inefficient (Index it! Figure out the equations!), but it's fast enough. And it works. So now I can use all eight channels for their own mixes.