The most disappointing thing about this thread/forum and Davidski's blog is the constant flow of t r o l l s who argue their personal theories that aren't supported by any data at all. R1b has absolutely nothing at all to do with the ancient Caucasus, either north or south. R1b is clearly intrusive to the Caucasus and lacks the age and diversity we would expect in the region. R1b is a hunter-gatherer lineage of Russia along with R1a. Outside of Armenians, R1b is at considerably lower frequency than the YDNA haplogroups that have been associated with the region, but also with the spread of farming. Sure a couple of smallsample sets in the north east Caucasus have shown high frequency but the caveat is that they are young founders. It's rather clear from the map that R1b was either native to Europe/European Balkans or Russia (steppes region in particular). Since the spread of the more successful branches of R1b are younger than the entrance of farming to Europe, one can only infer through the data, it arrived from the Russian steppes, that is, until the data points otherwise.
To the OP, I think R1b- both M269+ L23+ and M269+ L23- are excellent candidates for Hittite, but also likely the Cimmerians as well. The Mycenaean speaking Greeks and Illyrian language speakers should be added to that list. The Neolithic period of the Balkans are unlikely to have contained heavy doses of R1b, and if they were present, they were likely archaic versions of R1b that were overrun by the spread of farmers who arrived from the south and east.