Ok, now the tricky bit - draw a polygon (button looks like a piece of paper with top left corner torn off - click a corner follow the perimiter of the board, must finish up where started or will get "illegal poygon" error or similar), name it GND, on both sides of the board. Your thru holes will connect them.
Click the Rubberband button, and let eagle connect everything up to GND. May even be to "ripup" the ground traces.
Have been playing with ground planes/polygons, all seems well, but once everything is routed, I like to ripup the polygons to make everything else easier to see. Interesting that running the CAM job on the board in this state (attached) works fine, and all the "unconnected" pads get connected to the ground plane just fine.
I added the ground planes last, and found that I could ripup previously routed ground traces as you said. In fact, I'd suggest doing so. Haven't tried it, but maybe adding the ground plane polygons first
would be the way to go...