Car transporter for Youngtimer overpass hire

Hello Forum, I would like to buy an Audi 80 S2 Avant and transfer it to my home. Since the vehicle does not have a TÜV, short-term registration marks fail. The distance back and forth would be 2000km. I can drive vehicles up to 7.5t, so I have driving licence class 3. I actually thought of a car transporter, because I do not have a suitable towing vehicle with trailer coupling. I would also rent a towing vehicle with trailer if it were cheaper and easier to do than a car transpo Does anyone have a good tip for me where I can rent something like this?