Ah man... I was just going to stop doing computer stuff for the day...
I don't know much about this or computer vision in general but I think these are relevant links.
https://en.wikipedia.org/wiki/Vergence#Convergence
https://inst.eecs.berkeley.edu/~cs280/sp15/
^ just the stereopsis parts
A wide convergence is for things far away (like stars in the sky light years away).
Narrow convergence angles are for stuff close up and make you go cross-eyed.
When things get too close they go beyond the "near point of convergence" making you see double.
It's good to keep things above the near point of convergence or it'll be hard to watch.
I found this formula in that eecs class (I filled in the variable names to make it readable)
baseline = IPD
convergence = (baseline / 2) / depth
If you could change the IPD for the video when it falls below the near point convergence, then it would avoid the double vision effect. The rest of the video could keep the default IPD. I think that would work in post since it's just for quick bursts when things get too close.
I know even less than @bacula8630 though so if changing the IPD or horizontal offset in post causes headaches then that's probably not a good route.
I think this all lines up but I'm not sure if it totally checks out. I didn't have a chance to change the IPD to test this setup.