1) Sanyo monitors are natively inverted relative to other models like Wells-Gardner or Electrohome. that's why they work with Nintendo games, which are inverted, and require inverters if you're swapping them in for use with other games.
2) Mario Bros., Punch-Out, and the PlayChoice-10s as far as I can tell all came with Sanyo Z2AWs, not Sanyo EZs. while there are some negligible differences in capacitors vs. the EZ, the Z2AW comes with inverter boards.
3) the inverter boards on the Z2AWs with Nintendo games have 2 separate plugs: inverted and non-inverted. I don't remember specifically which is considered "inverted" in Nintendo terms, but these will have the monitor signal plug from the game board plugged into the one to not invert it.
4) you can do away with the inverter board completely by just plugging the monitor signal straight into the monitor instead. the mode in which it's used on Mario Bros. it's basically just a pass-through, and only introduces another cold solder point of failure later when you start dropping colors cause the solder's cracked on the headers.
any other information you hear about this other than what I just said is wrong.