Hi, welcome to BYC!
So as it turn out... chickens didn't seem to get the memo about when they should or shouldn't do certain things. It's completely normal for them to molt whenever their body says "go". Though it can be very frustrating to us as keepers, especially like that picture above!
What is the protein % on your game bird feed? Too high as in 30% can be just as detrimental to the kidneys as too much calcium fed long term to birds not in lay. Both or either *can* (doesn't mean will) cause gout (different types) and even kidney failure.
My recommendation is not more than 25% protein... with 20 being probably sufficient. Awesome that you're providing the extra protein.

Many don't realize that feathers are made of 90% protein and the amino acids it contains.
I ALWAYS feed flock raiser with 20% protein and 1 ish % calcium... because I always have chicks, broody's, molting hens, juveniles, roosters, and layers present in my flock. I do mix in a little extra game bird or turkey starter to get about 23% protein when I am hatching as it has been shown to give better hatch rates. I was quite impressed with how fast most of the girls returned to lay this year, verses when I used to feed layer... which I won't buy again as it simply doesn't meet the needs or goals for my flock. I do provide free choice oyster shell on the side for layers. Also noting though, that all birds are individuals and age may impact things. None of my ladies had what I would call a hard molt this year. So maybe they wouldn't return to lay as fast if they had. But I DO truly believe the higher protein DOES impact molt for the positive.
And I will note that I don't use artificial light. If you happened to be using light and it went out suddenly that could trigger molt... just for conversation piece.
Also might as well note, since we are talking about it... that light bodied breeds like leghorn will do fine on "layer" (16% protein) while birds like Rocks, Orpington, and RIR will do better with about 18% protein on a regular basis since they are heavier bodied and feathered.
It's hard for us to see their change in demeanor and such during this time that makes it clear just how taxing molt can be.
Hope your birds recover quickly.
