We are flying from US to Sveti and don't think it's a big hassle, though we are stopping in AMS for a bit first. Austrian and a few others offer one-stop connections from most U.S. cities. Doesn't Austrian fly from MIA? Can do MIA-VIE-TGD and it's a 45 min drive from there. Even more carriers fly to DBV, but that's definitely more of a hassle (who wants a 3 hour drive after two flights?).

Turkish is another option to TGD. I believe Montenegro Airlines flies to select cities - I remember seeing Frankfurt and Paris when I was booking my flights.