I now have answers to the questions I posted earlier.
I got a flight from Kiev, and got a visa-on-arrival at Tehran airport ($135 USD for an Australian passport, ouch.)
Took a train to Shiraaz and went around the bike shops. The interesting options are:
CG125 Clones (~$500). Quality not bad.
CGL125 Clones. (~$800). These are bored to 125 - 200cc. A bit bigger than the CG, with slightly better suspension, disc brake.
DR200 Clones ($1400 - $2000). Nice bikes, more power and much better suspension. There's also a 250cc version. Problems are: 1. 10L tank, 2. nowhere for luggage.. you might get a small rack on some models.
There are also Indian bikes. Bajaj Boxer etc. Probably also a good choice.
I bought a CGL150. I put a slightly bigger front sprocket and some extra padding on the seat, and it was good for cruising at 90kph. Not that comfortable, but did the job.
I was told at multiple bike shops that it's not possible to have the bike in my name, due to being a foreigner. So we put it in a friends name.
The bike shop goes to the police and applies for documents. It takes 1-2 weeks until they are ready, then they are sent to the address of the registered owner. You buy insurance in the bike shop too (cheap). The bike comes with a plate and you can drive away.
You can drive all over Iran. The police stopped me several times for checks, but only wanted to see my passport. Noone seemed alarmed that a foreigner was driving a [locally registered] motorbike.
A couple of notes on driving in Iran: Traffic is ok. Roads are generally good. Fuel can be bought easily, don't worry about the fuel card. When they fill the tank, they'll ask if you have a card, if you don't, they'll use one of their own, and the price is slightly higher. This is perfectly routine.
I wanted to take the bike out the country into Turkey. However, this is not simple. I spoke with the head of Customs (Mr. Noushiin, I think) at the border near Urumia (Summer 2015). The registered owner must apply to the Iranian Auto Club for foreign plates. They are in Latin letters, not Arabic, and are valid internationally. There is charge of around $50 USD, I think. With these plates, the bike can leave Iran (without it's registered owner) for up to three months. However, it must return within three months, or the owner recieves a fine equal to three times the value of the bike. I asked if there is any other way to export the bike, apparently there is not. Only the Iranian goverment can export vehicles (such as Iranian cars sold abroad). So I sold the bike and carried on.
*Regarding entering without a carnet, it is possible:*
You must make a deposit of 3x the value of the bike into a bank account. They will give you the details at the border. The process can take a few days. You must then return through the same border crossing to recover your deposit. While this is an official procedure, they told me they prefered travellers to use the carnet, as it's faster and easier. But, this is also an option.
I drove from Shiraaz, through the mountains to Yasuj, then to Isfahan, then to Kermanshah, again through the mountains. From there, into the Kurd area, close to the Iraq border (beautiful road and great views), lake Marivan, then down to Urumia and Tabriz. Here I sold the bike and left the country. All done on a two week visa with no planning as such. It was in the middle of summer, but temperatures were pleasent due to the altitude. Look for the green areas on Google maps.
Photos here:
https://goo.gl/photos/DpEkJ34wid9w11b28