I re-installed the Milsat feed and found something I'd not noticed before. The beacon on 7662.5MHz has both left and right polarisations. The right is about 150Hz high of 7662.5 and the left about 180Hz low. The modulation looks the same on both.
Note that this can lead to some confusion over the aiming of the dish. If the polariser is not set quite right, the peak response may not be on boresight. This is due to the polar pattern having peaks either side of centre for signal of opposite polarisation to that set. However, if you have an SDR or analyser, it's very easy to null one to set the polariser, remembering to re-peak the dish as you go. The plots below show LH & RH optimised. I seem to get much better X pol rejection to RH than LH but the feed etc was a very early attempt so may explain the difference.
LHCP
RHCP
Below is an extract from GD Satcom approval tests showing X polar rejection. I see a much exaggerated and distorted double hump on X band, probably due to the non-ideal feed. The peaks are also much wider spaced due to the lower frequency (7.5 vs 29G).
1.2m dish, 1dB NF LNA