The box in question is the large one on the bottom 
How to cover the lettering on this box?
+6
This large, wooden, wine box has “good bones” but I want to cover up the text so it’s less noticeable/legible. I tried staining the top a dark walnut but it didn’t quite work like I wanted. The goal is to make it look a bit aged, but not painted. I really want to preserve the wood grain look.
Any other ideas I can try? A combination of techniques maybe?
You could always paint it. What type of finish (shiny of flat) do you want? Do you just want to cover up the lettering and what shade do you prefer?
try a gentle sanding over the lettering -- looks like it's been 'burned' into the wood ... if it's a stain, a stripper might remove it to the bare wood.
You can always age the wood with a torch. Plenty of videos available.
https://www.youtube.com/watch?v=C2tjNhuL6To
If you sand just the one panel, when you stain it you might discover that the wood "grabs" the stain differently than the other panels. Sanding, especially with a coarser grit, opens up the wood cells more. I would sand the entire box using the same grit. You may have to experiment with this.
The torch idea suggested earlier would add a unique touch and likely remove any trace of the lettering.