(( You guys are basically Bourbon Democrats; consistently isolationist and free trade as the main unifying factor between your various types of conservatism you display. But Bourbon Party is hardly a decent name, and in context is just as civil-war-baiting as Southern Nationalist or Regionalist or this or that would be; as it basically means "we'll rise again, just like the Bourbon dynasty".
The Free Trade Party would be too on-the-head, the Traditionalists would be too nebulous, States Rights is regionalist-scare re-inciting.
You could stick it to the labor movement with the National Union as opposed to actual trade unions. You could evoke Warren Harding with the Normalcy Party or the Normal Party or something like that. Evoking that and the Regular Democratic ticket from period in real life you could be the The Regulars or Regular Party.
As much as I like some of those, I have to suggest the one you'll probably latch on to that I don't like as much, the Independence Party.
Other options include Free Americans, Citizens Party, and Citizens Independence Party.
Longshots include the Plutocratic Party, the Timocratic Party, The Plutarch Party, The Gilded Party, The Patrician Party, The Patrons Party, The Patriarch Party, The Bourgeoisie Party, The Gold Party, and the Honorable Party.
Finally, on the Dempublican note.... the Res Publica Party, RPP (Res Publica Party), or Catonian Party ))