I've done all of the above.
Like I said, the problem only appears in the Operation Mannerheim's Skold campaign that comes with TSF. I have an independent nation set up which is perfectly selectable in the initial drop-down menu. But when actually entering the campaign (at the first mission screen) the aircraft has the proper paint scheme, but the national markings do not match the nation it should be under. Nor do the callsigns.
So as an example:
I added VF-103 with F-14Bs and the US Navy as a Sweden-allied unit and nation in the campaign's data files.
I can select "US Navy" and VF-103 in the "Create Campaign" screen. However, once I actually do so, and start the campaign, said VF-103 Tomcats do not have the US Navy markings and callsigns they should, but rather the markings of the Forsvarmarkten (or however you spell it). From what I can tell, for some reason the game is confusing my Tomcat squadron with one of the default Gripen squadrons, and I'm not sure why.