The components on the board(s) inside that head are likely tiny and surface mounted by robots. Even trying to desolder them would likely burn up more than what you fried.
Most electronics repair of items manufactured in the last decade or so involves board swapping. You simply unplug terminals, unscrew the board, and replace. (I repair medical equipment. Maybe audio is different, but I doubt it.)
I have on two occasions managed to remove and replace tiny surface mounted stuff. It was a huge PITA. I did it as a favor to medical facilities that couldn't afford new equipment. I wish I had never agreed to it. I managed to get it done. But it sucked. And I got pretty lucky both times. They should have gotten new circuit boards, but that would have cost about 2/3 what a new piece of equipment cost. You're likely in the same situation. If they'll even sell it to you, a new board will set you back a couple hundred. You may as well grab another one.
To be fair, every manufacturing operation I've seen in Japan and China does the soldering with robots, but the rework/repair with people.