If all you want to do is move items over, Don't connect the switch with Atmosphere to the internet.
Have both consoles open the game and do local play. You don't need to be friends or anything, just need to be within ~2 meters
Edit: a little more information:
Just don't connect the switch with Atmosphere to wifi at all, you dont need it, nor do you want it. I'd use the physical game in this switch, start the game, play it until you can travel to a different island. After that You'll backup your save file with JKSV, then you'll find something to edit the save file ( I don't actually know how to do this, I'm not the one who plays ACNH). Make sure to keep a backup of it, just in case what you changed doesn't work.
Once you've edited the file you'll restore it in JKSV, if that works open the game again and make sure that works.
Then you'll use the digital copy on the real switch, start the game, both go to the airport and travel using local play. At no point do you need wifi with Atmosphere so dont worry about the DNS and all that. Just keep both switches within 2 meters of each other while travelling.