As our trip is only one way this was out of the question for us. ;)
Searching for a solution online we soon found out about Hussein from Overland to Iran. We got in contact and explained him our travel plans. He wanted 600€ for this service and told us we were only allowed to stay seven days in Iran with our car when entering from Azerbaijan. This was way too much and especially not long enough for our stay in Iran. Also he told us this when we were already in Baku, meaning a giant detour to enter through Armenia.
Not knowing what else to do we decided to visit the Iranian ambassador in Baku! We got invited for tea and he made some phone calls in our behalf. In the end he assured us that it would be no problem and we could acquire all the needed documents at the border. He also organized that Muhammad Safari (09141526002) would await us at the border in Bilehsavar and handle all the paper work.
Leaving Azerbaijan took less than an hour but then the problems started. This had nothing to do with our car, the problem were the two walkie-talkies we had with us. Apparently your not allowed to bring in radios... To stay in touch when we get separated (especially at border crossings were they only allow the driver to remain in the car) we use these. More and more people were involved until finally some high ranking dude showed up with his driver. We had some tea with him and could finally clear the issue and keep our walkie-talkies. He got us to the front of the line and we got our passports stamped and were officially inside Iran. This took us about two hours, but our car still wasn't registered.
After this little "detour" we could start getting our paperwork for the car settled. Worth mentioning is that the car is registered on Genti but I was driving into the border post. So everything was under my name. I tried to tell them this but they didn't care and told me it was fine this way ;).
First I had to sign some document in a little hut, where they translated my name to Farsi, lol. They copied this into a big book and I had to visit the shack next door, where the copied this into another big book. Then our fixer, Mr Muhammad Safari showed up and we told him where we'd like to exit Iran to Turkmenistan. He didn't speak any English but with some help and hand signs we were able to communicate. He disappeared with our car documents and the papers we got on the Azeri border for half an hour to return later asking for money. He wanted 400$, I offered 300$ which he immediately accepted, damn should have gone lower... Anyway still way cheaper than Hussein.
With our money he vanished into the building with all the chaotic counters for about an hour. I checked on him twice and saw him stand in line on different counters. Maybe if you spoke Farsi and had a lot of time on your hand you could do this by yourself...
So he emerged with a our car license, an insurance all in Farsi, and a staple of papers, on them where multiple stamps and even a hologram sticker ;)
It seemed they had used our Azeri papers as reference, as they had added an AZ in front our license plate number.
Next was another shack where they copied my name again, this time into a computer. Then the form had to get stamped on another desk and half of this we had to hand out to the guy manning the exit. And that's it!
All in all it took us about three hours and 300$ to get the car across. We now have official papers and are allowed to stay for the whole time of our Iranian visa.
We snapped some pictures with Mohammad and drove on!
Edit from the future: To leave Iran to Turkmenistan on the Bagjiran border we payed a dude 30$ to unlock the gate for us. No idea if this was for him or an official payment. The ambassador had told us we would need to pay around 10$ for every day over six days we stayed in Iran... Anyway, the gate was open and we continued!