Yo there's something REALLY useful for soft reseting Galarian Moltres (and probably Articuno too but I haven't tested it out for it yet)
The IVs seem to be generated when you load the bird in. So at first, it seems like IVs are locked... but you can reroll them by just flying to the same area again.
So as a result, you can save before you encounter the bird (saving saves the bird's position), throw a master ball to check the IVs, and if its a spread you want, then close and reopen the game, and then catch it in the ball you WANT! If it doesn't have the IVs you want, just fly to an area on the map, and the IVs are now rerolled!
I used this to get a 1 Attack IV Neutral Natured Galarian Moltres (synchronize seems to work on the birds too)! I kept it in the Luxary Ball, but I also have a picture of finding its stats with the Master Ball to prove my point, identical stats!
Here's another set of images earlier when I was soft reseting Galarian Moltres to prove my point: one is in a Master Ball, the other an Ultra Ball, and they have the same IVs.
I'll test this with Articuno soon as well, but this seems to be the best method to SR for the birds. BTW, for Galarian Moltres: it's really easy to cheese it if you just fly to the train station on the isle of armor, it'll spawn in a place where it flies in front of the grass near the Dojo every time.