Tool alignment on material flipping

Hi,
I have recently needed to mill some gear wheels and due to the complexity of them, they needed milling from both sides. Quite precise too. However, aligning the tool on the center hole after flipping the work piece proved quite the task. So, for future projects, I want to simplify this process.

Using the touch probe sucked, It needs to be calibrated to 0.1 mm precision, which I simply could not do with what I have, neither could I use it from the milling screenset in the UCCNC software, switching screenset requires re-homing and is a big hassle.

My new approach is to get a laser pointer and align it so it points exactly at the center below the tool at about 10 mm above the work piece, however, this requires a very fine-beamed laser pointer that does not burn the wood piece.

Any suggestions on both methodology and/or choice of laser?

//Kind regards.