Also I do wonder if LEO are cool with you pulling off the closest available turn off on a highway for both parties safety, and if that's communicable. Seems like something that should be the norm.
I've been pulled over on the highway plenty and I just get over as soon, as far, and as neatly as I can. If they want me to do something else, they'll let me know. I do try not to drive on the shoulder any more than I must because I don't want a flat tire. So, I will signal my intent and slow down in the traffic lane as much as I can if it's possible to do so. So... Maybe down to like 20-30mph before I pull off.
In town, I do what I can to stop under a street light or I might pull off if there is an immediate place to do so, then stop.
I also would show my hands and get out of the car if asked... I think that was the big problem here.