I just checked on the geometry of an offset dish:
When the elevation rotation axis of an AzEl mount is situated exactly in line with the line Center of dish face (C') to Deepest point of the dish (D), so that it lies
exactly at the beam center line, then the received satellite beam of an inverted offset dish
is exactly at the same height as that of a normally mounted offset dish.
See the attached picture, with the lines C' - D exactly in line, for both normal and inverted setup.
When the axis is situated higher up, e.g. behind the deepest point or behind the center of the dish, the inverted dish receives a HIGHER part of the beam. So in that case inverted mounting is advantageous: the higher the elevation axis is situated, the more advantageous.
This goes for a fixed mast, and also for a motor setup.
How much higher? For a fixed mast this could be calculated, with inputs:
1) distance dish face to elevation axis
2) distance top of dish to height of the axis (measured at dish face)
3) height of the dish
4) offset angle of the dish (or width of the dish, in combination with 3.)
Alas, 1 and 2 are not measured very easily (but not impossible!). So I'll leave the making of the formula to another time, or another person.
For a motor setup, the advantage diminishes the further you go from due south or due north, I assume. But I think even with a 90 degrees motor rotation, you would still have more than half of the advantage, I think.
But I'm not sure; I have difficulty to visualize the consequences of dish inversion in that situation. It might be dependant on the MOTOR-axis elevation angle, so on your site latitude, if I'm not mistaken.
On a motorized setup with a bend in the shaft, you can add an extra effect by changing the angle of the shaft bend, as Trust showed.
By that, the position of the dish elevation rotation axis
relative to the height of the mast gets higher than in 'normal' position.
That would be the new starting point for the dish's elevation rotation axis, so there is your advantage...
I hope I've helped to clear things up a bit about the principle(s),
Greetz,
A33