... early nuclear bombs are too heavy to put on a sub, and any subs trying to cross the Atlantic after 1943 will be detected and destroyed.
No, they're not too heavy. An early nuclear weapon weighs about 5 tonnes - that's well within the capacity of any ocean-going U-boat in this timeframe. Consider that each torpedo weighed about 1.5 tonnes, and they would normally carry at least a dozen.
As for the detection issue, I'm not convinced it's as clear-cut as you make out. Even at the end of the war, putting to sea in a U-boat wasn't a death sentence for the crew. A U-boat which avoided the major shipping routes as much as possible might have a decent chance of making it to the eastern seaboard of the USA.