Cleaning the boat also means you get to crawl all over and inspect nooks and crannies - which mostly serves to confirm that no surprises lurk in unknown places! (every little bit helps when offshore
and it is blowing a gale!).
In regard to repaint idea, am not entirely sure what the wood / finish is - but certainly the look is (to my eyes) "of it's time". I would start with a test piece of a small panel (that locker under the cooker looks ideal) to see what sticks to it! the idea being that even if plan A does not work as well as hoped that you can keep testing until something sticks and even if you end up having to replace the facing (or the entire locker lid!) with something that doesn't match it won't matter visually. Plus whilst you are testing for durability you won't actually have to do any work!
Me would simply sand down the facing (past any finish, whether varnish
or another coating) to get a good key (if it is a "solid" plastic laminate that simply looks like wood then no need to get past it, just past the shine)...the key is the key! - once you have a good key then use a decent primer (something universal - wood, metal and whatever) to give it a coat or 2. The test being whether you can scratch it off with simply a finger nail - or anything else up to not damaging the underlying hard surface (everything marks if you gouge it sufficiently!). Unless you are dealing with a high wear area (like a work surface or floor) you really only need the finish to be as robust as paint on wood. The surface you will end up with will look like paint on wood, which means it won't look like a polished gelcoat
moulding or a plastic laminate - IMO all the better for that as looks less clinical (imperfections and all!).
I would definately keep the wood trim with the wood finish though - I think in the US it is called the Herreshof(sp?) look as breaks up the acres of white.
The interior woodwork of a boat should really only be a once in a lifetime thing to redo, unless the interior is really abused. and no need for "marine" paint.
Just be careful about not seeking perfection (an excercise in frustration - especially as when you redo one bit amyway it makes other stuff look worse, inlcuding the stuff that up till then you thought looked ok!) IMO the most you will achieve is an overall look that says clean, neat and tidy and well loved - but not showroom fresh (even when new your boat did not look as crisp as a 2013 Beneteau
etc - a bit more character though!).