Yeah, there’s no real concrete way to do that kind of stuff, but you’re on the right track with distortion. Try different methods of shaping the sound itself, automate compressors and stuff, bounce a copy, use it, etc…
He probs did just what ypu say and distorted and / or compressed a long 808.
I find that using small amounts on many different distortions can help u shape then sounds more delicately. But sometimes with this its just finding the right sort of distortion and eqing afterwards to remove any muddy or piercing freqs
honestly tho it’s fairly easy to make a distorted 808 but the way to make it stick out in the mix as an all-encompassing monster bass is all about mixing the track. truss me daddy
there’s the fundamental and then there’s the third and whatever those peaks that the bass consist of are called
you look at what they do on a freq meter - see how they behave and move, and then you pick those peaks and try to remove them accordingly on other bits in the mix by subtractive eqing
there’s also a nifty trick of having your whole bassline pitched up one whole octave and then let that play silently triggering a sidechain
this will sometimes work as ‘protecting’ the low mids because it means the key the sub would go in, is free to do so obviously one oct below, but it will still clean it up in a way that is in tune in terms of the upper freqs
it’s sort of the same school of thought as having another instrument play the notes an octave above it to fatten up the bass - or like when using autotune a lot, having a synth play the same notes under it to fatten it up (think danja)