Michael Solomonov has a recipe for amba in Israeli Soul — though he calls for ripe mango and doesn't ferment it, just cooks it down with spices/onion/garlic and adds lemon juice and salt at the end. Looking at those directions, it sounds like it would produce something very syrupy, which makes me a little suspicious.
He also name drops Galil brand jarred amba, which they apparently sell at Goldie. (I think I had the sabich there — but it might have been some other sandwich with amba.)
The best sabich I've personally had was in Detroit, from the bakery (Naba Brick Oven Bakery) that Marcus Samuelsson visited on his PBS show ("No Passport Required"). It happened to air just before I took a trip home. The Iraqi-style sabich there is served on a diamond-shaped bread called samoon which is thicker than pita but quite light — very pillowy. Closer to Turkish doner kebab bread than pita — and I think close in thickness to the Italian rolls @ambra posted above.