Trimming Veneer around Tweeter

Hello,

New member, and in the process of my first speaker kit build (building my own enclosures). My question is around veneering, specifically around the tweeter recess. Experimenting on a test board, I cut the outer recess circle and the inner through-hole for the tweeter and woofer, then veneered the board. Routing out the through-hole is no problem for either. But for the tweeter, the depth of the recess (3 mm) is less than the height of the bearing on my flush trim router bit, so I can't use that to trim the veneer.

Should I route the smaller hole after I veneer (I prefer routing the hole early when there is less at stake build-wise), or is there some tool/trick to trimming the veneer around a shallow recess?

Thanks