I'm not sure I can be of much use to you in recommending an off-road route from Trabzon to Fethiye as we travelled with our belongings and two dogs in a van from the UK to Edirne then hugged the coast until we reached Kas.
A useful site for info would be
Paola Volpera of One More Mile (OMM) is un tout circular bon oeuf (all round good egg)
He helped me with our route.
Also try Dave-In-Turkey on this forum. He is near Fethiye.
Would love to meet upwhen you get over here and hear of your travels through Russia