Not sure where you have been getting this information from, but a couple of points:

You cannot enter South Ossetia from Georgia.You can only enter from Russia. I did this in 2010 in my car and it's a very nice trip.

Abkhazian embassies in the UK, Germany, Greece?? Where did you get this idea? None of those countries recognise Abkhazia as a country, so of course there are no embassies there. In 2010 I got an entry permit over the internet from the Abkhazian Foreign Affairs Ministry and then got a visa in Sukhum (Abkhazia). You can only enter Abkhazia from Zugdidi, or from Russia.

There is a new asphalt road to Mestia (Svaneti). Beyond is dirt tracks which I doubt are really suitable for such a heavy bike.

Nagorno Karabakh is great to explore with your own vehicle. Many areas are officially off-limits, but I found that nobody checked and I drove all around the area without problems. Many of the roads are in quite poor condition, but nothing too bad. The road along the Iranian border is a very interesting (shocking) drive.

Ingushetia, Chechnya, Dagestan are some of the most interesting parts of the Caucasus, I highly recommend visiting.

The road from Quba to Xinaliq is asphalt and fine for a bike.

Perhaps you are interested in a write-up of some of my trips in the Caucausus here:

Azerbaijan, Georgia, Abkhazia:

Stage 19 – Azerbaijan, Georgia & Abkhazia: The South Caucasus | EurasiaOverland

Adygeya, Karachayevo Cherkessia, South Ossetia:

Stage 20 – Russia & South Ossetia: The North Caucasus [1/2] | EurasiaOverland

North Ossetia, Ingushetia, Chechnya, Dagestan:

Stage 20 – Russia & South Ossetia: The North Caucasus [2/2] | EurasiaOverland

Good luck.

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EurasiaOverland a memoir of one quarter of a million kilometres by road through all of the Former USSR, Western and Southern Asia.