Reduce line interference pickup, then dig for every dB
With a maximum size dish and minimum noise figure on the LNBF alrady, you need every dB you can get.
First the easy part:
Add a line amp at the dish, right at the LNBF output connector.
Now put a 10 dB attenuator at the receiver end of the cable (make sure it passes DC without attenuation.)
This will keep your signal to noise ratio at the receiver input close to that at the LNBF output.
Now the harder parts, USE CAUTION if you choose to point the dish at the sun, don't hurt your LNBF!
Check your dish shape to make sure it focuses well at the LNBf (use string from the focal point to the dish when the LNBF is directly over the dishs' center) or for best accuracy paint the dish with chrome paint, put black aluminum at the LNBF feed (not touching the feed) to catch the sunlight
so as not to damage the LNBf
, aim dish at the sun to see the focal spot)
*caution hot*
Fix any problems, then repaint the dish grey and remove the black aluminum protecting the LNBF.
Make *sure* no obstacles can get into the beam (rain?

)
Tweak your aim as perfect as possible.
Even try "skew" (rotating the LNBF (yes, even with circular polarization) or slightly tilting or moving the LNBF toward/away from the dish to get better focus and absolute minimum pickup loss/reflection at the LNBF. We're talking small changes in signal here, but you're desperate I think. These measures wouldn't work on perfect dishes or LNBFs but there are none of those around.
Use the bit error rate (quality) meter to measure your progress while trying these. They will be time-consuming and tedious, with small improvements as a result.