I am glad to hear that you are working on the Float Left option (who knows maybe one day I make a website in Persian) and agree that if we have to choose between keeping things simple and having mega-menu functionality then simplicity is preferable.
The additional item on the mobile menu bar, is, I believe, essential and although people may not be missing it now, once it is provided they will find great uses for it. I think that whatever menu item you put on the mobile menu bar next to the slide-out button will on average get a higher number of visitors than the items of the slide-out menu. In order to keep things simple and uncluttered on small screens, however, it would make sense to limit the number of these additional items to one or maximum two: it/they should act as a strong call-to-action and not a replacement for the slide-out menu.
Thank you for your time and efforts
Maziar