As an American I would stick with HSBC, Lloyds might be good for those in Europe or UK, but I've heard some hassles with them as well.
You can drive up to the HSBC Jebel Ali branch and it's a nice option. You will pay the Salik but at least you can avoid the nightmare in Deira and most everything now is done on-line anyway so the drive to the branch should be a rarity. Customer service in is India somewhere but it's 24/7.