Sand it...
I bought a 1986 Hunter 28.5 last year. While it doesn't have yards of teak, it does have teak handrails, companionway hatch, helmsman seat, and Edson cockpit table. All had been allowed to go to seed (that is, they had been finished with something in the past, and it was shot). I decided to sand all of this with an orbital sander starting with 100 grit disks and finishing up with 220 grit disks. The whole thing took about 2 hours and it came out great. It was much easier, and better looking, than I had hoped. I'm a long time user of Cetol so that's what I put on last -- as, like Fred, I don't want to be doing this again