Nope. The Republicans were the new face of the Know Nothings. They were not anti-slavery Whigs. The Whigs that merged into the Republican party were mainly the hard core central bank/protective tariff/corporate welfare Whigs (of which Lincoln was a fervent member). A few other weird northern parties, such as the Anti-Mason party, also threw in their lot. The unifying theme of the Republican party was that it was a pro North and anti South, a purely sectional party. On every issue the Republican party aligned itself with the interests of the North. The party didn't even run any candidates in the South. The legend that the Republican party was somehow an anti-slavery party was invented after the war.
You nailed it.
First, the Federalist/Whig tradition is America's genuine conservative political tradition (the Jeffersonian/Jacksonian tradition has always been radical).
Second, the Republican party was formed as a single-issue party and that issue was "anti-extensionism." Many of the early Radical Republicans were actually anti-bank and anti-tariff, etc. (Thaddeus Stevens held the same position on money that many of today's neo-Confederates do).
After the Civil War was over the party's initial founder, Alvan E. Bovay, even suggesting ending the party (since it had achieved its purpose) and creating a new single-issue party based on prohibition and temperance.
Don't tell me . . . neo-Confederate . . . right?
The roots of the Republican party date to the "Free Soil" party of the early 1850s. It was primarily a 'mid-western' party opposed to the expansion of slavery to the territories and in favor of Homesteading of the Western territories.
The Kansas-Nebraska act, pushed through by the Democrats with some Whig support ended up breaking the Whig party. Pro-slavery expansion Whigs such as Alexander Stevens became Democrats and anti-slavery expansion Whigs such as Lincoln became Republicans. It was only later that the Abolitionist factions also signed on with the Republicans as their best alternative.
Many of the former Whigs in the Republican party then maintained their Whig roots of being in favor of protective tariffs and internal improvements as did the former Whigs in the South who switched to the Democrat party. The position on slavery, or more accurately, the expansion of slavery was the driver, not economic or trade policy.
As to not running candidates in the South, that is not quite true either, depending on how you define "The South." In the Upper South states like VA, KY, and MO, the Republicans did indeed run candidates. They didn't do well, but they did run for office. In the 'Deep South' in the 1850s, it would have been suicidal, literally, for any politician or his supporters of any party to oppose slavery or the expansion of slavery in any way. It would have been like a Jew looking to run for office in Iran today. They would have been killed.
In the South, even the Deep South, politicians supporting the same economic policies the Republicans supported -- high protective tariffs, Central banking, and internal improvements could and did get elected --- Alexander Stephens of Georgia, who became the Confederate Vice President, was a prime example.
The differences all came do to where they stood on slavery.
Hummmmm. Funny thing is that in 1856, the first year a Republican ran for presidenton an anti slavery expansion platform, the "Know Nothing" Party's presidential candidate had the vast majority of his support in the South.
Hummmm? Maybe you want to check your premises. 
Except that Republicans were opposed to expansion of slavery to the territories, and opposed to requirements for free states to enforce slavery. That made them against slavery.
Slavery was the key issue for the south, which is why southern states that gave any reason for pretended secession, all cited slavery.