My main argument is that domestication (of wolves and speculatively of "hobbits") is essentially a matter of selecting for individuals that don't socially mature to the point of trying to become dominant in their social group. In human terms it is the equivalent of keeping them at the emotional equivalent of a pliant seven to nine year-old, eager to please their parents (and, yes, I know that all kids in that age group aren't pliant, but a lot of them are). Young chimps (up to age three or four) are pliant and trainable too. A lot of zoos have them doing all kinds of tricks. The problem is that as they grow older they mature socially and try to dominate the humans around them. That's why you rarely see adult chimps in animal acts.
Granted, a wolf-pack is not structurally the same as a chimp troop or a band of humans, but all three species do have a period of "childhood" where they accept direction from and cooperate with more experienced individuals. Freeze them there socially, and they can be controlled.
The route to domestication or slavery (and this is kind of a hybrid of the two) would be essentially the same as that for human slaves. There are routine thankless jobs in any society that people would prefer that someone else do. The difference is that the semi-human slaves can't rise above their station to play an independent role in society and can't interbreed to become part of the dominant group.
I think you're coming at it in very general terms, when the core idea - hominid domestication - is a pretty safe bet. As the Russians have
shown fairly definitively, domestication in (at least) placentals appears to involve a single set of genetic triggers. Once activated - and they are activated by the easy expedient of eliminating the most aggressive individual every generation for a few generations - the result is remarkably consistent across very different species. The genes can take a long time to reach full expression in the entire population (thirty generations, as a ballpark figure), but it will happen. It would have happened historically except that for every male slave killed a female one would end up pregnant by her owner. And that slavery is difficult to maintain on a scale of centuries.
Generation time is a justifiable objection, but there are ways around it. Human generation time is 15 years at the longest, and arguably could be more like 13. Island species tend to go a little slower, but earlier hominids tended to go faster, so ten year generations are not unreasonable. To get them domesticated, that and the lack of cross breeding is more than enough. Assuming humans start sometime around 4000 BC, they should be more than ready as a domesticate when the "Romans" turn up.
The only part I'd have a big objection to is the timing - a Rome that appears to be no later than 500 "AD." So far as I know, in that period it was very unusual to see multiple breeds of the same species in the same place. There were many breeds, but they were localized breeds - the breed of a particular region. In a very real way, distance was the original method used for preventing strains from being interbred. Once people in an area decided what a cow should ideally look like, that naturally and gradually became the way they looked. It was only much later that I'm aware of European societies having multiple types of everything, and even then it was mostly a case of importing breeds as much as creating new ones locally.
So I don't think there's anything wrong with your vision for the species, per se. But for myself I'd need to assume their presence in multiple regions for five centuries
at minimum, and probably more like a millenium, to allow breeds to diverge enough that they could be traded. There's every reason to believe that the "ideal hobbit" would differ place to place - albinos perhaps in northern Europe or Japan. It's just a matter of time.
When is this "Rome" they are visiting? If it's circa 1500, that's simple enough, but I'd have to stick with the naysayers if the Romans have fifteen kinds of pixie at a time they didn't have four breeds of goat.