As I said, in the "goode olde dayes" we used 30 degree up tilt and it worked well... Lessening the up tilt may increase the gain for the lower angle passes but will also decrease the gain on the higher angle passes. So, it is a "trade off" no matter what you do!
Sorry to sound like I am quibbling... but that last sentence implies the idea of an equal "trade off". But the tradeoff is not equal at all and may be missing the point here.
A LEO satellite pass does not need gain at "higher angles" because the satellite is by definition 2 or 3 times closer to the ground station (+6 to +9dB stronger). But one does need the gain at lower angles where the satellite is much further away.
An up-tilt of 30 degrees is throwing away excess gain where it is not needed (high angles) at the expense of low angles where every single dB -is- needed. So there is no real tradeoff... A lower angle (about 15 degrees) is more-or-less optimum for LEO's with fixed tilt and modest gain beams.
To actually quantify the exact best angle (which will depend on the actual beam's own beamwidth), it is simply to up-tilt the antenna no more than the angle at which the gain on the horizon LOSES say less than 1 dB. Note, this is not half the published "antenna beamwidth" which is usually a "3 dB" beamwidth. It is much less than that, less than half the 1 dB beam width. You can measure this by setting the beam no higher than the upangle that loses less than 1 dB to a signal on the horizon....
Something like that... Bob, WB4APR