Yes - all good ideas, folks. That's why I love this site.
Really, the key element in the whole thing is... time.
If you simply put the excess browns aside in a corner of the yard, they will all break down. I've also used palmetto and cabbage palm fronds as the weedblock layer in sheet mulching projects instead of cardboard.
I tend to view the extra browns as good fungi food and put them directly on the ground in my food forest.
Finer stuff can be piled next to a main composting area and mixed with greens as they become available. Again (I said this in another
thread and in my book), don't use any cow or horse or goat or alpaca or any grazing animal manure or straw/hay from off-site. The risk of long-term herbicide destroying your gardens is very high.