That boat really cleaned up nice! You should have shown us the "before" picture before!
Bleaching the wood is a good idea and should not hurt it much but I would not use the Tip Top Teak if you're worried about getting the louvers too thin, as it will remove a lot of the soft grain. I've also used Deks Olje #1 & #2. It's not bad but will not hold up like Epifanes.
One tip when you're applying varnish, prop the door up on one end so the louvers are horizontal. That way the varnish will fill in the low spots in the wood. After about 6-7 coats, it'll be pretty smooth. You can wet sand any rough spots between coats with 220, or scuff it with a red 3M pad.