When the old Federalist Party collapsed after the 1816 election, Northerners joined Democratic-Republicans for the 1824 election, and just managed to elect John Quincy Adams.
But unity didn't last long.
By 1828, Adams ran (and lost) as a National Republican, a party which also fielded candidates in 1832.
By 1836 National Republicans had become Whigs, a party which lasted through 1852.
After Whigs collapsed, abolitionist Republicans became the main anti-Democrat party.
So the sequence was:
So, from the Founding of the Republic until Goldwater in 1964, the "Solid South" was solidly Jeffersonian / Jacksonian Democrats.
During that same period, the North was represented by Federalists, National Republicans, Whigs and then Republicans before turning, in the 1960s, solidly Democrat.
Hate to get involved in a rather abstruse discussion, but I think you’re falling prey to a rather common mistake.
There were initially no “parties” at the founding, other than federalists and anti-federalists, neither of which line up particularly well with the parties that later developed. Or, rather, the federalists at the Founding all pretty much went into the Federalist Party, but the anti-federalists split, with some joining, at least initially the Federalists and others signing up with the Republicans.
The Federalists had a long decline as the opposition party agter 1800, but pretty much killed themselves off, at least as a national party, during the War of 1812. There followed a period from the late teens thru 30s where the contention was primarily not between parties as such, but more between Jacksonians and anti-Jacksonians, both groups fully paid up members of the Democratic-Republican Party, the only one left standing.
This party split in two during the 1830s, forming the Whigs and the Democrats. So IMO the Whigs were every bit as much a continuation of the original Democratic-Republican Party as the faction that kept the Democratic name. And so were the Republicans who eventually succeeded the Whigs in the role of opposition party to the Democratic machine.
BTW, as you probably know, the 1850s were a much more complicated period in American political party history than any other. The Whigs, Democrats, Know-Nothings (American) and Free-Soil parties all played a part.
And of course during the 1860 election there were four parties in the running, northern and southern Democrtats, Republicans and Constitutional Union, which was more an attempt to revive the Whigs than anything else.
Most critically, national politics, and particularly party politics, did not consistently break out into a real north vs. south split until the 1850s. As southern aggression (which they viewed as only self-defense) got more intrusive, the North developed as a self-concious political region, replacing the previous East and West, with the West normally aligned with the South.
It's worth noting that one of the factors in the Federalist collapse was the Hartford Convention, where the idea of secession was merely discussed and rejected, appearing nowhere in the final report of the convention. It was enough, though, for the south to loudly proclaim them as traitors. Here's what one Virginia newspaper said about it in 1814:
"No man, no association of men, no State nor set of States has a right to withdraw itself from this Union, of its own accord. The same power which knit us together can only unknit. The same formality which forged the links of the Union is necessary to dissolve it. The majority of States which form the Union must consent to the withdrawal of any one branch of it. Until that consent has been obtained, any attempt to dissolve the Union, or obstruct the efficiency of its constitutional laws, is treason-treason to all intents and purposes."