Looking for flush mount audio jack to put on desk

Have not seen exactly what you are looking for but why not do what you have in your PS section... hear me out.

Get the extension cable with the 1/8" female jack, drill the hole exopy it in with the plastic part flush with the desk, leaving the metal jack just proud of the surface, get a metal washer whose inside diameter matches the outside diameter of the metal portion of the jack, spray paint it a pleasing, either matching or contrasting color and glue it around the jack.

You could do something very similar with a wooden bung (plug) though it would require a drill press to mount the jack into the bung and some decent finishing skills. Actually this could be really cool if you used an oversized bung in a contrasting wood but does require a fair amount of woodworking skill.

Another cool approach which is what I would do but I have a full woodshop about 150 ft from my chair is flip the desk or remove the top and drill a hole in the desk from the bottom with a forstner bit (the size of the outside of the female jack) and stop when the point just breaks through the desk top, the point should leave a perfect hole for the metal upper portion of the jack to sit either level or almost level with the desk surface. Then just fine tune the fit with a standard bit or an exacto knife and glue the jack in place.

Anyone of these three approaches properly executed would yeild better results than any sort of flush mount audio jacks (if you can find a female 3.5mm) I have seen. They tend to just be utilitarian metal chunks.