Boy, it's hard to believe the oil would leak up hill if I'm picturing the photo correctly. I'd have to guess you are leaking out the gear box gasket because it's not sealed properly and the splash from below is leaking out. I think your idea of leaving the inspection plate off and seeing what happens is the way to go.
From high school chemistry the perfect gas law equation is PV = nRT, or "Pressure times Volume = amount of gas times a constant times Temperature (Rankine or Kelvin)". In a fixed volume like a gear box, pressure goes up proportionally to temperature. But the temp is on the Rankine scale or 459 + your room temp. If it's 70 deg. F, that's 530 R. If the oil heated up 100 F, that'd put the oil at 630 R or a increase in temp of 18%. That means the pressure inside the gearbox went from 14.7 psi to 17.4 psi. There would be some pressure build up but we still have gravity so I don't see how the oil could travel uphill.
Bruce