I was having a dive into my Aftershock's settings last night after having not done so for a while. The main thing I found which I didn't know before was how much of a difference the drive pre/post blend makes. From this source audio blog post:
Navigating the Neuro Desktop Editor with One Series Drive Pedals
Here is a little known fact: within each of the pedal’s two drive engines there are two separate drive circuits. The DRIVE P/P BLEND offsets these drive elements often increasing one while decreasing the other to create mostly subtle, but sometimes very dramatic differences. The amount of impact this control has on the tone varies depending on which drive engine is being edited.
For the "Bass Tube Drive" engine, the "pre" drive is a very natural sounding, touch-sensitive overdrive, whereas the "post" blend is a kind of distortion/fuzz that kicks in very easily (i.e. without needing to "dig in" at all). Varying this blend lets you trade off touch sensitivity and an organic sound vs having a more consistent amount of drive regardless of dynamics. I first tried setting the blend to 100% pre (i.e. a setting of 0 in the app), but eventually settled on a 75%/25% split (i.e. a setting of 64) for a bit more bite.
More generally, the settings I focus on in a rough order of priority are:
- Drive engine
- Drive pre/post blend
- Drive level
- Clean blend
Voice & voice frequency are also worth a look, but generally I only touch these if there's a noticable EQ bump/cut that I want to tweak. A good example of this would be giving a PI/muff based engine a bit more of a mid boost since I don't like its scoop, but personally for that sort of sound I just sidestep that by using a "Bass El Raton" or similar.
I love being able to set the max drive level; it's awesome being able to get a much finer-grained level of control for drives where you don't intend to their highest gain settings.
With regards to the OP's specific question on fuzz/muff sounds, the "Bass Big Pi" is probably the closest thing, but for the music you've described the "Bass El Raton" with high drive could work quite well for you.