Hello, a bit late to this thread I am afraid.
What choice of op-amp do you have? The CMOY uses - what? A buffer IC with high input signal demands, or a high gain IC like the TL072?
Hold on, here:
http://tangentsoft.net/audio/cmoy-tutorial/parts.html#op-amp
As you see, it is the OP132/134 amps he recommends, more specifically the OPA2132PA. I would go with that if I was to build the Cmoy, many audio DIY people use these IC:s and say they are good. It seems it is also stable, not prone to oscillation.
An OPA2134 PA costs 4€ at my "expensive-dealer-but-has-a-large-searchable-product-database" (elfa.se). This is with the DIL-8 case, which will fit a standard 8-hole socket. Probably not that hard to find a cheaper one.
Hope you soldered an IC socket in, in that case changing is easy peasy. Just earth yourself before changing.
Second, I would change the volume control to an attenuator. tubecad.com has a good attenuator for a good price, called the "TCJ stepped attenuator". A smart solution for an old problem, most other kits are waaay more expensive. And not as smart of course.
http://glass-ware.stores.yahoo.net/netcjstat.html
Third, for low voltage applications, you could get a bunch of OS-CON capacitors to replace the standard caps. They can actually change the sound quite a bit for the better.
Then, fourth, I would try driving the amp with a battery. I like battery PSU:s, and the Cmoy is built to be able to use them.
All these changes will improve the sound