I can’t recommend it as a good idea, but you could run the mirrors in a way that will get there.
Mount the laser parallel to the X axis at the edge of the table. Use 1 mirror at 45 degrees to bounce it parallel to the Y axis, say just inside the Y rail.
Mount another mirror on the YZ plate to bounce the laser straight up, inside the XZ plate.
The third mirror is on the XZ plate bouncing the laser back along the X axis towards the tool head.
Now, if your Y axis goes out of square because of the motors being out of synch you will miss the third mirror and burn a hole in your ceiling. If your Z axis is oit of square you will miss the tool head and burn … something. This is why its a bad idea.
It could be possible to mount the laser tube to the gantry. This at least avoids the possibility of motor misalignment causing bad things™ from happening, but that’s a whole new kettle of fish to have the laser tube mounted on a moving platform. I think a laser tube inside the beam braces would look awesome, but in a “holy crap that’s dangerous” kind of way.
Another thing to keep in mind is that those morrors need to stay clean even regular dust on them will damage them when that laser hits it. Those mirrors shoukd stay inside an enclosed machine where they are not exposed to dust, let alone possible chips from a CNC milling operation.
I want to run a CO2 laser at some point, but it’s not going to be on a V1 chassis. It will br a dedicated machine.