Yeah, when I built my first Peter Blasser paper circuit I remember trying some vintage mylar caps and getting crazy results compared to polyester. And I remember reading about the original ResEQ caps being polystyrene and that making a difference (smoother maybe?). I think Mylar and polystyrene are also much more susceptible to temperature fluctuations.
Maybe you can temporarily install header sockets so you can swap out different cap types and see what happens? Or solder wires to the bottom of the connections and work on a breadboard?
Re: your power header question, you should be able to! According to multiple sources there it L/R symmetry on these connections. You just have to
also flip the connector horizontally, not vertically. I would write “+” on the board or use red sharpie/nail polish like
@grey said, and also def check it with a meter.