Advice on paint deep in wood grain

Restoring an old medicine cabinet with an apparently rough life, pulled from a junk pile. The interior was coated in thick white paint. I stripped that with a water based stripper, then sanded back with 80grit. That went pretty well but there is still quite a bit of paint deep in the grain, almost acting as filler in some of the larger/deeper fissures

Thinking of a few options:

• Manually picking out the paint, possibly with some heat. Probably not feasible as there are so many little flecks. A stiff brush helps, but so far not much luck
• Keep sanding back, which would probably require removing a lot of material to access all of these deep grooves. I'm leaning towards this, but also holding out hope that there might be a way to loosen/flush it out without losing too much wood
• Consider wax/stain options that might even it out. Least favoured option. I suspect the white might not take stain well, and pop even more. My original plan was just tung oil finish, which I'd still prefer

Any advice on ways to handle this?