Gonna do what I can to help y'all... as somebody who rather likes the game, I can tell you right now that the game is buggy as heck (less buggy with plus but plus is still getting updated every now and then for a reason) and can be a bit of a hassle to set up on some computers, so I can't say this all surprises me, but I also find the game is quite worth getting working so I wanna help y'all if it proves possible!
I've played this game since I was very young back when it first released, and I can tell you I've never had a problem setting it up on any PC. The game has its bugs, pretty much all the bothersome ones being fixed by Plus.
The way Plus is installed via GOG is awkward and poorly-laid-out, but if you can find the buttons to do it, and you make sure you're not accidentally running the wrong version, it should work great.
This aside, I agree with your troubleshooting advice.
Also, in regards to OP's question about Christmas Chronicles -- No, but if you copy all the .J2L files from it and put them in your Jazz 2+ folder, you should be able to play through the Christmas Chronicles levels in Plus via the "Holiday Hare 98" episode in the game's episode selection menu.
The reason for this is that The Secret Files includes a file called Xmas98.J2E which tells the game to include a "Holiday Hare '98" episode, and it points the game to the level files from the Christmas episode. But it doesn't actually have the levels unless you copy them over from Christmas Chronicles. I believe if you copy a file called Xmas99.J2E from Christmas Chronicles, then you get a "Christmas Chronicles" episode, but it's functionally the same as Holiday Hare, just with a different name and artwork. The reasons for this are convoluted, and it basically boils down to the fact that Christmas Chronicles is a slightly improved European re-release of what was originally released in the USA as Holiday Hare '98. (Which is a reference to Jazz 1's two entirely distinct freeware Chrismas episodes, Holiday Hare '94 and Holiday Hare '95)