There are two significant points regarding Iranian visa applications from the UAE.
Firstly, I think you have to be resident here to make a visa application. Therefore, you will probably have to apply from your country of residence (not your country of nationality). Having said that, when I was in Erzerum, Turkey, I heard that the Iranian Consulate there was a possible source of visas for travelers. Maybe, you would have a similar opportunity in Addis Ababa or somewhere along the way.
Secondly, when making the application it wasn’t necessary to hand in a passport. You fill out a form which is sent to Tehran and you get the reply within a week or two depending on your nationality. This, at least, enables you to make plans and get the necessary visas for alternative routes in case of rejection.
Have you phoned the Iranian Embassy anywhere to ask them? In my dealings with Iranian authorities at the Consulate and inside Iran, I always found them to be friendly, polite and helpful.
I hope you manage to get a visa.