Visited here last weekend, and noticed an interesting alignment.
If you stand in the centre of the fort with Arthur’s Seat behind you on the horizon, then you find yourself pointing at a small hill on the horizon to the east. I haven’t figured out what it is yet though – it may of course just be a natural hill!
This alignment roughly passes through the entrance, beyond which is a large boulder.
From your photos, could the small hill on horizon be Whitekirk Hill with it's cairn ?
I think you are looking at North Berwick Law. If it is the small prominent hill in this photo.
themodernantiquarian.com/post/86883/chesters.html
The hills on the Eastern Horizon are displayed here
goo.gl/maps/2woj8v4Pjp32
L to R North Berwick Law 187m, The Bratt 78m, Whitekirk Hill 74 m.
The Garleton Hills to the South are unlikely to be what you are referring to. Likewise the ridge stretching SE on the other side of the A1 and Haddington seems unlikely from your description. I don't think (from a faded memory) that Traprain Law (to the SE) is even visible from The Chesters.
This is a view of North Berwick Law across The Chesters looking ENE.
goo.gl/maps/NemhMDdtyRv