Haha I feel you — goats are something else, always acting like they’re starving even with a whole pasture in front of them! I’ve got a mixed flock too and went through the same thing trying to simplify feeding.
All Flock feed works great for the chickens, ducks, geese, and guineas, just toss some oyster shell on the side for the layers and you’re good. But for goats... not so much. They’ll
eat it, of course, but it’s not great for them long term. Too much poultry feed can mess with their copper and cause issues like urinary stones, especially in wethers.
What I ended up doing is feeding All Flock to the birds and keeping the goat feed separate — I just feed the goats twice a day in their own space and try to distract them when I’m feeding the birds. Not perfect, but it keeps things mostly sane.
If your goats are getting hay and have green stuff to browse, they really don’t need grain all day — they just
think they do

. You’re definitely not alone!