One little known fact is that a motherboard from a Mac LC575 will fit in without modification. It has a 33MHz 68040 (LC040 really - no maths co-processor)

So I tracked down a Mac LC575 and put the board down next to the Color Classic board. Same size and connector.
Left: LC575
Right: Color Classic

Not much work to do there - so I put the motherboard in and fired it up. Unfortunately, it started up with a bus error. The LC575 tries to set a resolution of 640x480 and the Color Classic can't do that - it is set to 512x384 in hardware....so we should be able to change it then eh?
Short answer - yes. There is an analog board modification you can do to the Color Classic which enables 640x480. Details here: http://colourclassicfaq.com/highres/index.html
In the end you just cut a trace, solder in a wire, remove a resister and bridge a jumper. Easy.
Follow the instructions on the site - be very careful with the voltages around the tube and analog board. Couple of pics from the site:


With the 640x480 mod done - I fired it up again - booted perfectly and it is really fast! Here is a pic of the machine after the changes - note the trash can is in the position of the old screen resolution edge.

NOTE: I did have to add in a capacitor to the analog board to bring the horizontal position across enough on the screen - but after adjusting it up - it is stunning. Details on the site above. Such a sharp little screen and a great little compact Mac to have around.
I also took the backing plate from the LC575 and trimmed it down to fit into the back of the Color Classic. The standard Color Classic backing plate doesn't quite line up.