Butter not mixing into dough

Hello! I'm making brioche. I let my mixer go a bit too long before adding the butter bit by bit at the end. It seems like the dough has too much gluten formation to let the butter mix in. Is there anyway to fix this?

My butter and eggs were room temperature as per recipe advise. It's so fatty my dough hook won't grab it now. Will I be mixing by hand forever? Thanks!