Have you tried rearranging the order of your effects pedals?

Yyou might have better luck putting the noise suppressor at the end of the chain rather than the beginning. That way it's suppressing the noise from the overdrive rather than just the guitar (which should be clean anyways)
You could also try moving the compressor to the front. That way you're compressing the guitar signal before it reaches the overdrive.
The effect would be that the signal reaching the overdrive will be hotter and able to sustain better rather than your compressor compensating for lower volumes when your overdrive is making noise.