Sorry, apart from McD's, there really don't seem to be many options, though I think if one asks, most places will probably be able to rustle up something to taste, as long as you are not in a hurry.
I do know that quite a few of the Kebab stands and similar places, do have some good vegi, pita/pocket bread options.
Matter of fact, the ones I have seen are really very good, they are made up as you want and generally, nice and fresh.
Downside being, they too, take somewhat longer.
Oh well, i guess, "if it's worth having, it's worth waiting".
On a completely different note, can't help but wonder why, in the vegi burger options in your link, they have
bacon as an extra