Winner,
Agreed. I was with you right up to when you typed this bit...
Most of the Romans who made it to the New World are soldiers, not farmers, fishermen, hunters or craftsmen. They don't know how to survive in this strange land.
The legions of Rome - from before the Marian Reforms, through the long death of the Republic, and up through 3rd Century CE - were simply crammed full of men with "civilian" skill sets. Hell, after the legions morphed from short service conscripts to long service professionals, you had a better chance of joining if you already were a craftsman of some sort.
You name it and a legion could do it; butchering, baking, or candlestick making. They grew or raised a big part of their own food, only buying bulk grains from suppliers. They made their own clothes, armor, and footwear. They had their own blacksmiths, foundaries, and factories. (Even now we still find buried caches of iron nails near legion forts that weigh in the tons. Keeping the boys busy making nails was apparently one Roman cure for the
cafard.) They cut timber, made lumber, quarried stone, fired kilns, and performed hundreds of other tasks.
I'd have trouble believing a thousand or so ordinary Roman citizens would possess enough skills to recreate their homes after a shipwreck. However, I'd have no trouble believing that a thousand legionnaires could so.
I do have lots of touble with this "caught in a storm off Iberia, end up in the Carribean" POD however. It's too far and would take too much time. A storm of enough severity and length to do the job would also be strong enough and long enough to sink a classical vessel well before it crossed the Atlantic.
And somehow landing in South America is even more implausible. Check the latitudes, you'll have to be well south of Morocco before you're "even" with South America and then you'd be in the "horse" latitudes. Storms blow out of that region, not into it.
A lucky or nearly fatal voyage for a merchant that opens the Canaries route across the Atlantic and starts a trickle of trade? Maybe. Thousands of refugee Carthaginians or the XXth Legion being blown off course to the New World? Never.
Regards,
Bill