You have a lot of positions received at very far distances.
I doubt you could improve your reception with the range you already have.
An LNA should not be used with the Flightfeeder, as they receive the GPS position via the main antenna.
Filtered LNAs would block the GPS signal.
Also an LNA can be a problem in regards to signal quality.
The Flightfeeders are already a system that is very well optimized.
I don’t think Flightaware would mind if you installed a quality replacement coax (LMR400), but as i said it’s unlikely to improve reception would be my guess.
You are limited by terrain already:
What is the Maximum Range I can Get?
If you feel like experimenting, i would suggest you build another feeder based on a Raspberry Pi.
Maybe with the rtl-sdr LNA weatherproofed directly connected to the antenna.
Then an rtl-sdr v3 as a dongle or even an airspy ;).
When you have it optimized, maybe find a location that can overlook the sea to the south of Sicily?