"So how does f2p have no fps drop if they swap the thorn and the emblem? Or is it because p2p has to move the emblem and f2p doesn't since they can request new ones from the goblin banker?"
Yes, on f2p the emblem can request new ones from the goblin banker.
"Could you not make it swap the thorn and emblem on p2p without the fps drop somehow? It's quite noticeable."
I can do it less, if need swap both and no fps if need swap one thing.