Did you ever manage to get it out? Struggling with the same issue on mine
I tried to pull that damn thing out about a dozen different ways for a month. I made special tools to grab it and twist it and lever it, but where it was located, you couldn’t get anything on it. I checked with everybody I knew, and an old mechanic friend gave me this:
Poor brake fluid all over it for a couple days. I had to make a funky angled funnel out of some paper rolled up because even that was hard to do!!
The reason it’s frozen in the hole is the greasy carbon crud is rock solid around the top and the O-ring. The brake fluid will eat that up in a couple days. Then I just tapped it sideways a couple times with a 5/8 inch wrench, actually very gently, and it started to move. Once it started to move, I could work it back-and-forth and eventually it came out. But it didn’t come right out or easily, I had to wiggle it forever, and eventually I worked it out.
CAUTION: if I recall, it’s a tiny 5.5 mm socket for the little screws that hold the electronic cap on. 10mm for the whole down screw and washer. The screws are made so they stay in the cap, but that bolt and that socket can fall right down in the hole when that synchro comes out. Guess how I know that. I have one of those five dollar telescoping magnets from Harbor Freight, and thank God, I was able to stick that down the hole and pick the socket out. It’s my own fault and my own stupidity, because 99% of the time when I’m working with something like that, I use electrical tape or masking tape and actually tape the joints of the ratchet and the extensions in the socket so they won’t slip off. Again, if I recall, right, I had three wobbles extensions on a quarter inch ratchet and a universal just above the socket, and you had to slide that in perfectly to get it to get to those screws.
Hope it helps
