Given that the technology probably existed, and given the probably conditions in Doggerland that you mention, I think even if the item in the illustration isn't actually a paddle, they more likely than not had some form of water transport, certainly sufficient to navigate around the coastal regions of Doggerland and what became the North Sea. And those spear-points in the picture - I don't pretend to be an expert, but those rows of barbs/serrations make me think of fish-spears or harpoons (and given that Star Carr was on the shores of a lake, that's probably what they were, although obviously they were hunting deer and other biggish game too).
I like your Greek theory - it may be a bit speculative, but it's the good kind of speculative. No aliens or Atlanteans in sight To me, it doesn't seem all that implausible. As you say, when Europe was still sparsely inhabited and largely covered with forest, travel via rivers was probably if anything easier than travel overland - it doesn't seem implausible that trade networks existed between the North Sea/Baltic and the Black Sea, especially when you consider that it wouldn't necessarily be a case of individuals having to travel the whole distance personally; trade could very likely have occurred via various middlemen. I'm a firm believer that goods and information in prehistoric, ancient and medieval times could and did travel much further and more routinely than most people probably suspect, even if the vast majority of individuals didn't travel so far. I'm thinking of things like medieval Islamic pottery and coins turning up in Canada (true, apparently!). It wasn't a case of Arabs visiting the New World, but rather Arabs trading with Vikings in Russia, Vikings in Russia trading with Scandinavia, Scandinavia trading with Iceland, Iceland trading with Greenland, Greenlanders making at least occasional visits to North America and having some limited contact with the Native Americans. I'm sure similar networks existed in earlier times too (we know there was limited contact between Rome and China), maybe in prehistoric times. Maybe not between Europe and the Americas (although you never know given when you were saying above about the "swarthy" Formorians...), but between Northern and Southern Europe doesn't seem like a stretch to me at all - in fact, it seems very likely to me.