I'd like some advice on how you think I should repair gaps between the boards. I was considering completely filling and then routing back out, or maybe trying to caulk them and shape the caulk. I'd see pros and cons to both.
Well, personally I think that planked wooded wainscotting in bathrooms isn't the greatest of ideas and I'd replace them, however...
Routing filler won't work (the filler will just crumble in places).
Trying to rout down to the floor level won't work, either, because the base of the router will limit how far down the wall you can get. And have you ever tried to route something fixed vertically to a wall? I've done it a few times - it isn't for the faint of heart or inexperienced router users
Routing to a straight line will require a guide batten to be fixed to the face of the wainscotting for the base of the router to run against - but if the planks aren't flat (i.e they are cupped and bowed) your router won't follow the original moulding lines and it will end up looking a mess
Routing will change the shape of the beads, because those weren't produced by routing and there isn't a router cutter which can replroduce that shape in situ on a wall
So, in my opinion routing really isn't really a feasible
If you are determined to re-use this wainscotting, then you need to thoroughly strip these to bare wood to see how good or bad they really are before making the final decision. It may be possible to clean the beads up using a home-made profile sander,
rubber sanding profiles or by adding one of
these kits (a Fein profile sanding kit) and some PSA (self-adhesive) sandpaper to a multitool. It will be a lot of work, though. After you've stripped them you may decide it isn't worth the effort, so maybe start with a small area first
The gaps can be caulked with paintable silicone (they are the bottoms of grooves, so it won't be that noticeable under a few layers of oil-based paint), but because it's a bathroom I'd avoid filler if at all possible simply because the wood is going to move with changes in moisture levels