Is there a reason you can’t bring your geometry into MeshCam from a DXF? It can recognize round pocket features as holes and drill them accordingly, and you can do similar in other CAM packages.
I’m not terribly familiar with Eagle’s output options, but you could draw the circle of the hole and have it treat it as a pocket/field to clear, and just set the depth through your material instead of just taking the top layer off the PCB.
If the Gcode is putting tool-paths on contours that you’ve drawn, rather than filling areas, then you’ll just need to account for your cutter diameter when making your circle for your hole.
What you may end up doing is several passes of features, each exported/extruded to different depths to achieve your PCB-engraving goals… one for regular trace-cutting, one for thru-holes.