I agree with the "try a different amp" suggestion. Once the "dirt" is in the signal, running it through a "clean" boost does little or no good. It's called a clean boost because it doesn't appreciably alter the character of the incoming signal (unless it also contains an EQ section of some sort) and doesn't add signal distortion. So dirt in, dirt out.

I've read great things about the Boss Katana line of amps, and they are very reasonably priced. The 50W 1x12 combo is just $219, which isn't much more than most good pedals cost....and less than some!