There's so much repetition in there. E.g.: (adi-json.adb)

    if not W.After_Key (W.Depth) then
        -- things
    else
        W.After_Key (W.Depth) := False;
    end if;
    -- ...more things...
    W.After_Key (W.Depth) := False;

And what's the deal with those filenames? If you replace adi- with TIMMEH, you'll see what I mean.

Code should be more DRY (don't repeat yourself).