I had exactly the same problem. If you take a look here (swipe right to see all three pictures)
https://www.instagram.com/p/CiXSQ5CLB1W/
you can see what our railings looked like. It took a hell of a lot of sanding to get 90 % of the varnish gone and then came the question what to do next ?
New varnish, paint, teak oil or something else.
A friend of mine, who is a carpenter, pointed me to Monocoat. Told me that is used a lot on wooden floors (so with heavy traffic on it), so I gave it a try. At the time I could not get the outdoor version (with UV protection), so on the pictures it is the indoor version, but by now I have received the outdoor version.
As you can see on the instagram post we put it on in September and since that time had a lot of salt air, rain etc, but it is still perfect. They advise to redo it after a few months to make sure you have covered every pores in the wood there is.
Am pretty sure it won't last as long as 12 layers of varnish, but the good part is that if I need to put a new layer of Monocoat I just need to sand it lightly and apply 1 coat of Monocoat (hence the name).
Some people say: 'isn't that what teak oil also does' but no that is not the case. Monocoat is a 2 component system. You get the oil and a hardener and the combination makes it last for a very long time. I am only 2 months in, but was told it will last at least one year, if not longer.
At the same time I just sanded the wood on the side of the boat, applied 15 layers of lacquer which means it should hold for quite a while, but if I ever have to sand that down...............i will be busy for days.