i'm corn fused. ....
heat (T) is caused by friction (u) . i can't take an equation and directly substitute friction for heat. and how does friction "cause" pressure, that's heats job? ln(P2/P1) = (ΔHvap/R) * (1/T1 - 1/T2). I'm not seeing friction in here. ironically, diff fluid mitigates friction, as that's why its there in the first place. I'm not certain how 4 more oz of fluid is going to cause friction and therefore heat. The only way more oil could be a functional part of your theory, would be the ΔHvap, but if it really was that much pressure (which its not, btw as more oil would be a heat sink as it touched the casing) that's what the valve is for. so, if your seal is leaking from pressure, its not the fluid, its the breather not working, and more fluid will not cause a breather not to work as it cannot be filled to full or close to it. the location of the fill hole is deliberate. notice its not on the top? its where it is so it cannot be overfilled and prevent any sort of drag or foaming. the gear needs to slosh thru it and spray it, not be submersed in it. plenty of space is maintained.
If they want you to fill below the hole, it's because the oil will expand a little with the temperature, and leak out if opened when warm, if filled to the edge when cold. If you feel a few drips leaking out of the diff hole on the off chance you open the plug when hot, is going to change the crash course the planet is headed on, by all means, buy a special tool to measure. I've given up on saving the planet. I'm sticking with my pinky.