Re-staining with a lighter stain
Try applying a household bleach full strength in a small area you've sanded. Chlorine bleach will remove dye without harming the wood, but it won't remove pigments. It looks like you've sanded away most of those already, so this may be a good final step.

Two part bleaches are another option; they're stronger but will lighten the wood. That's usually not a problem if you're going to stain the piece, but it will tend to homogenize contrasting grains. The potential upside is that these bleaches can decolor some pigments, which is a lot less work than trying to get them out of the pores.

For the spaces the sander won't reach I'd try a chemical stripper along with a brass toothbrush. Painter's tools (5 in 1 tools) are also handy because they won't gouge easily. Plastic putty knives are even safer, if less effective.

It's not magic, but using a gel stain might help. They sit on top of the wood to prevent blotching, but that means they have a fair amount of pigment added. It's not going to give coverage like paint, but it may disguise small amounts of the previous finish.