I would think it’s possible to get work with East European companies, are the Baltic states East European?
pay is probably not now as bad as it was, but still lower than UK domestic work. 
however I get the desire for travel and adventure, so fully understand where you’re coming from. Contact some companies and tell them, although I feel you’ll end up tramping round Western Europe more than going to far flung places, Milodon mentioned much of that work being done by even cheaper Russian and Turkish drivers, Recently I’ve seen many more Ukrainian, Turkish and Moroccan truck about.
The figure Milodon comes up with seems to match what a Lithuanian car transporter driver I was talking to last year was earning, but only on working weeks. I think you’ll find drivers from other countries like Romania and Bulgaria are on less though.
As Reef said why not look at the music tour and event companies, at 28 with no ties I think you’d be an ideal candidate. I’ve seen Fly by Nite, Brian Yeadley and Conference Haul advertise in the last few months.
Another thing to look at would be covered car transport, I know companies that have been out the Ukraine, Russia, Northern parts of Scandinavia in winter, tours of Europe from Scandinavia to Greece and all points in between, obviously takes somebody willing to train you though, but never know until you go and knock on doors.