The chorus limiter portion looks weird, opto isolator kind of biasing the clipping diode bridge. What are the characteristics of the distortion that sound awful? Is it shear high frequency sounding or low fuzz that muddles the distortion? My first guess would be to unsolder the two coupling capacitors C11 and C12, isolating the op amp bridge portion. Try two red leds opposing between the capacitor lifted, they will soften the clipping characteristics, that's a start.
Changing the op amp will define some overall tonal change. I copied an older MXR distortion pedal from the 80's and found an NE55xx (single op amp) really improved compared to a TL071 or the stock 741 .. that circuitry used germanium diodes for clipping that worked well with that configuration.
Trial and error will eventually get what your hoping for, two considerations, firstly, are electronic components available where you live? Secondly, is the circuit board durable enough to desolder components, a 25 watt soldering iron should work best.