Right tool for butcherblock cut

Putting some 1 1/2” butcher block in the laundry room. Putting in a sink, but want to preserve as much counterspace as possible, so planning to do a positive reveal undermount sink with a drop in cover panel that allows the sink to “go away” when it’s not needed.

Seems the best way to do this is to make one clean cut that allows me to use the “scrap” from the sink cutout as the cover panel. Problem is trying to make a thin kerf cut (think it needs to be around 1/8”) precisely.

Can’t find conventional router bits that work (1/4” shank screws you up), so found that some woodworkers use end mill bits intended for metail in CNCs and with adapters in routers. Also found some folks with similar issues using a dremel (which has 1/8” bits to begin with) with a “router” base that dremel sells. Finally, I can just try to make a precise cut with jig saw (perhaps circ for straight runs), knowing I have little margin of error for sanding, etc…. would probably upgrade my jig saw before attempting this.

What would you do? Dremel seems silly… leaning towards just using saw, but fearful its going to look like crap. Won’t attempt 1/8” bit in router unless I’m really confident the mount is solid (have a hitachi router if it matters).