I see similar issues. Clearly EK is being stingy (Or AS is being stingy under direction of EK) I assume it is EK. (I almost wonder if AS internal systems are given a quota, say 10 F slots on EK per month) limiting fallout if every EK seat happened to be open.

I have flights booked to DXB. I need the flight DXB-SEZ, so I am willing to drop my SQ J+F flights and take EK, but I have the following problem:

Even if EK J is open SEA-DXB or other city pairs, DXB-SEZ has severely limited space (with AS) (EF shows X4-9 on almost every day)

July has no open space to SEZ with AS.com
August has scattered dates.
September almost any day is open for SEZ
October only has 2 open days and they don't work for me.
November has 4-10 days.

Since EF is not useful in finding space, I am stuck checking AS.com daily which is ok, but not great.