Would Reconstruction have turned out much differently if Lincoln had not been assassinated, or were the problems between the North and the South too much for any one leader to overcome?

I believe that Reconstruction would have turned out much differently had Lincoln not been assassinated. It is true that cultural differences existed between whites in the North and the South, but, except for the slavery issue, the two groups were not that different. Many white Northerners had supported slavery: abolition was not a universally held principle in Northern states before the war, though after the war the North unified around extending rights and freedoms, such as the vote, to blacks.
Where Reconstruction took a hit without Lincoln was in race relations. Lincoln and the early Reconstructionists wanted to create a more racially equal society in the South. They wanted the former slaves to have a fair chance to integrate in the South with the vote and with educational and economic opportunities.
Unfortunately, after Lincoln was assassinated, Andrew Johnson, the new president and a Democrat, took a harsher view towards black rights. For example, he left it up to the states to decide whether they wanted to grant blacks the vote. Further, because many Southern leaders thought Johnson supported them, they instituted what were called Black Codes, binding blacks to work on farms without being able to quit, a situation that outraged Northerners as slavery under a different guise.
Because of Johnson, Southern whites were able to create a rigid white/black caste system which alienated Northerners, and more importantly, made life much more frightening and difficult for blacks. While the same might have happened under Lincoln or thereafter, the likelihood is that all blacks would have started their freed lives with the vote and greater protection so that they would have had more equality with Southern whites.