I've found this bit to be the key to trimming the veneer out of the driver holes: https://www.amazon.com/gp/product/B000K2G69M/
I'll cut as close to the edges as I can with a utility knife and then clean it up with that. Just don't push too hard or it will eat into your material.
Whiteside Router Bits SC28C Flush... https://www.amazon.com/dp/B000K2G69M?ref=ppx_pop_mob_ap_share
I think you're looking for one of these.. Instead of a bearing, it just has an unsharpened nubbin on the end.
Ignore the picture of a dado; that's clearly incorrect.
knife and then sanding could work, or something like this if your recess is 1/8" deep or more.
Which design is that looks like RS drivers?