If you have a string instrument of any kind that needs fixing, a mistake you made in building a new instrument that you need to "disappear," or a question about the ethics of altering an older instrument, ask here. Please note that it will be much easier for us to help you decide on the best repair method if you post some pictures of the problem.
Any thoughts or recommendations on repairing this damage around a sound hole on a Taylor guitar?
The owners playing style has worn the wood out from between the inlay.
My idea is to route out the damage and replace the wood tinting it to match then cover the area with an auxiliary clear pick guard.
I would try to clean the bare wood between the rosette rings with deionized water. Once it looks ok, and it's dry, coat the wood with CA to provide some protection. It's not going to look new again but you might be able to keep it from getting worse.
Clean the wood as best you can with an eraser and a mild bleach solution. At that point you could put a colored shellac to restore the color and finally drop fill with a clear polyester resin finish or CA. Ideally the shellac would make any drop fill reversible. Certainly the CA would be reversible but the polyester would hold up a lot longer. This is a factory made guitar, might as well make it last. After the drop filling I'd probably add a mylar pick guard strip that could easily be replaced as it wore out.
I was about to write exactly what David King wrote, so I won't... Gel CA glue would be trapped and held in place to some degree by the raised purfling strips.
Drop-filling with CA is a bit of challenge for me anyway. The medium or thick viscosities seem to work better but patience is the key. My best results come when I lay down a thin layer over the area at the end of the day and leaving it to set up on it's own over night. Multiple coats will have time to shrink down this way.
If you're in a hurry get the accelerator spray that won't cloud the finish, mask off the area carefully, spray a light coat, let it flash-off completely (10-20 minutes) then apply your medium CA from a pipette (you can toss it out if the tip gets contaminated from the accelerator). This assures that the CA cures from the bottom up and won't develop internal crazing or bubbles.
Since it's summertime in SA you might try a bottle of Solarez from a local surf shop. That should be quick, tough and won't shrink back. It's essentially what's on the guitar now.
When a customer asks me for a cosmetic repair, I often think "You can always make it worse." Many times, a cosmetic repair doesn't quite end as nicely as you would like and just draws attention to the problem. There's really no harm in a working instrument looking like a working instrument. If you use it, sooner or later, it's going to show. That's okay.
This is not really a cosmetic repair. Nick, the owner plays, amongst other styles, a very percussive style we call "Boland Bop" and it is wearing the sound board out around the hole quite aggressively. The edge is about to wear through and then the hole size will begin to change with, I reckon, all sorts of effects on the sound.
So it is a case shore it up now before the edge crumbles completely and it starts looking like Willie Nelsons guitar.
You could carefully color match the spruce with pigment powders and then fill the gouged out areas with clear epoxy. The epoxy will build quicker than CA and be less likely to turn white. Or as others have suggested build up the area slowly with CA.