That wood is in really rough shape and FYI many pros would advise that it doesn't make economic sense to try to fix it up, although it might seem sacrilegious they'd recommend striping out the old and installing new (if necessary having custom millwork done). I don't like to see old wood head to landfill but I would tend to agree if that one area reflects the condition throughout.
While I think it would be possible to make the wood look lots better — by cleaning out the old filler (a hellish job), bleaching the staining (IF bleaching works), filling with a colour-matching filler or stainable filler, then refinishing — the labour involved would be considerable and if you were paying someone to do it the cost would, I'm certain, be prohibitive.
Both options are honestly quite expensive but the first might actually work out to less believe it or not because of the much lower labour cost.
I'd like to keep a fairly natural bare wood appearance by finishing with a matte hard wax oil only.
I think you need to be realistic here about what condition the wood is in versus what condition you'd like it to be in. As the saying goes, no plan survives contact with the enemy ;-) While "hard wax oil" (whatever that is, the manufacturers are very cagey about revealing what they're really made from) is fine as far as it goes, like most clear finishes and especially penetrating finishes it's best applied to clean sound wood, which this isn't.
My advice, if you feel you have to retain the original wood trim, is to fill divots, prime it, undercoat a cream colour and then use "gel stain" or another coloured varnish on top to make it look somewhat like wood..... possibly not that different to what was done in the 60s! While it may not seem very satisfactory this is probably your fastest, cheapest and best option given the constraints.
When I sand these holes, I am getting black streaking in the direction of sanding:
It's hard to be certain but I think you're revealing dark staining rather than causing it. This could be iron staining from the original filler.
(Additionally if anyone has any good advice about how to get sandpaper into all those trickly little corners that would also be appreciated.)
My oft-repeated advice here is that stripping is preferable to sanding when it comes to removing old finish. This is even on flat tabletops, it goes double for complex mouldings (triple for carvings).
If chemical stripping is not an option for you I would strongly recommend looking into using a heat gun and shave hooks, these are purpose-made finish scrapers that come in various shapes to allow scraping of various profiles.
Even though neither is what you'd call a fun job they're far, far preferable than trying to sand something like this back to bare wood.
