Given that the aircraft antennas are linear (and not likely to change to circular - at least not in our lifetimes), I wonder if your CP ground antenna is working better simply because it has some better rejection towards the ground reflections ?
The only simple approach that I can think of is to provide an antenna that rejects any signals from below the horizon. The problem is that you would want to accept the signals from just above the horizon from distant aircraft. You have a very fine line between where you want maximum sensitivity and rejection. Probably not practical.
Ref. "Airborne Measurements of Electromagnetic Wave Reflections from Land and Sea Water", Allen L. Johnson, AGARD Confernece Proceedings No. 269 (AGARD-CP-269), paper 11. Might be of some interests... there's probably better references (I just happen to know this one).
Another, more expensive approach, would be to use multiple antennas on the assumption that if the direct and reflected waves are cancelling at one spot, they might be combining constructively at another spot. This would require an active receiving system and wouldn't help in the reverse direction.