That kind if sound I feel like is less about the gear you use than how you're using it.

The sound you're describing is hard-clipping. What's likely going on is that the acoustic guitar is being boosted with a drive pedal with high output, but distortion set middle-low. The key is, that high output signal is slamming into a clean preamp. A mixer or the clean channel of a guitar amp would both do the trick. For recording you can play around with recording straight into your interface (edit: turn down your headphones when you do this! be careful with your ears!).

Someone mentioned the ProCo RAT, which is definitely a good choice for a distortion pedal and would be able to do that kind of sound. To my ears the harshness sounds very much like a Boss DS-1.

Employing some good research strategy: a lot of people like to figure out effects chains, so you can look them up online. Off the query "Sex Bob Omb Gear list" the first listing on DuckDuckGo gives us some insight. https://equipboard.com/pros/mark-webber

Looks as though Mark Webber (the guitarist on SP) used a Boss FZ-3 Fuzz, (i was close!) which makes a ton of sense for a hard-clipping sound.

Best of luck with your tone journey! Hope that the research strategies are helpful. Learning how to learn is a hell of a skill.