Paint the teak with Brightsides that matches your topsides.
That's actually a good idea, it's often recommended to distance cruisers who are going to the tropics and don't want to deal with teak maintenance. The only thing I would add is that you seal the teak in epoxy first, sand with 120 and varnish it (but you only need two or 3 coats, not 8), then your prime and paint with Brightsides. That way, years later, the paint can easily be stripped from the teak and it is not soaked with paint into the grain. Preserves resale value if the teak can be restored to 'brightwork'.
Because I over-engineer everything... I would remove the teak rub-rails all together so they can be fully sanded and cleaned prior to epoxy sealing on all sides as well as within the screw holes. Then varnish and give it several weeks to cure (you'd be surprised at how long varnish stays soft). It sounds long and tedious, but you'd be way better off doing this indoors over the winter rather than on the boat. Another bonus... I'm not sure how your deck is secured to the hull, but if there is an overlap flange it will collect dirt, grime, and mold up behind it. With the rubrails removed you have a great opportunity to wire brush out that gap and fill/level with 3M 4200 (which can be sanded). Also, epoxy pot the screw holes. Doing all this with fresh bedding compound when the rails go back on ensures no leaks from the screws.
