OK, I've been searching over at PlanetFigure for references to painting these soft figures.  The OP of this thread mentions using thinned PVA glue, followed by primer, then his finish colors:

https://www.planetfigure.com/threads/airfix-soft-plastic-napoleonic-figure.362997/#post-1174436

I'll keep looking for other tips and share them as I can find them.