please don't get too hung up on prehistoric migrations that may or may not have happened.
This is the 21st century. There has been a nuclear war. A raging Atlantic, that may or may not have huge seabeasts, insane hurricanes and tornados, radiation. Back to the question: how do you cross it?
A Zeppelin is great because it's old-skool tech, can be filled with brahmin-gas, and can avoid the waves and sea-beasts. Downside is that savage lightning storms would potentially blow it away/turn it into a flameball.
Old-skool warship has to negotiate all of the above, BUT is armour-plated, steel, has weapons. How to man it/run it though.
And we're overlooking the obvious 3rd choice: submarine. Surely, hidden out in the depths, they would have avoided the worst of the nuclear war. And they are designed to run for months, years. A sub or two could still be seaworthy 200 years later (with a little maintainence). Has the advantage of avoiding the huge waves, radiation and storms. Still has to face sea-beasts, if such things exist. But I'm sure seabeasts have learned not to try to chew on a sub, bad for your teeth
I vote submarine.