I was the sole power on that continent, with plenty of room to expand to the best spots RIGHT before discovery by the other civs, who miraculously had the ability to sail ocean tiles hundreds of years ahead of me
Not miraculous, I'm afraid, but rather entirely predictable. If you're isolated and there are several AI civs together on a continent, then they'll trade their way through the tech-tree faster than you can research through it, even if you have a superior empire. Factor in the early game research sacrificed to get yourself ready for war, and you're likely to end up some distance behind.
One solution is to beeline for Optics (and then Alphabet) asap, and sail off to find them to get in the race.
In a completely isolated start (ie. with no neighbours whatsoever), and unless you've landed a really strong starting island, I reckon its the only way to go. Since you don't have to worry about military until Astronomy is discovered you can concentrate on research (including the appropriate buildings and wonders) to ensure that you get to them before the AI civs get too far along the tree, so that you've got something to trade for the techs you've bypassed. Up to monarch at least (I haven't tried it on higher levels, but it might still work), this is a great way to win a totally peaceful game.
In your case, with the Americans next door, you could have gone either way: war first and wait for them to come, or Optics beeline and war later with the tech advantage you get from trading. I don't know which would have been better, but it sounds like you've done alright for yourself.

Incidentally, one great advantage of isolated starts is that you have a chance to make your diplomatic relations from scratch, which can make planning for a diplomatic victory much easier.
You can survey the relationships on the other continent(s) before deciding who to make friends with, and so avoid the "You traded with my worst enemy" penalties. You can also give in to your friends' demands for assistance in war (or start wars and draw in friendly civs as allies) to gain the "shared military struggle" bonuses without actually having to fight.
And, if you don't manage to bag a religion yourself, you have a good chance of getting your friends' religions spreading in your cities thanks to your Open Borders agreements.
