IIRC, the suspension, including the rear shock, was significantly upgraded on all of the 2013's over that on the 2012's in preparation for the bigger motor, which then didn't arrive on time, so didn't turn up in the RT's until a year later, so I'd suggest you might find it'd be a bit of a backward step to put a 2012 rear shock on a 2013, even if you do use an RT Shock on your ST!!
You'd be much better off putting a 2013 or newer rear shock on; but
even more streets ahead by installing an a/mkt shock, especially if you get to specify your loaded weight and riding style, so that they can then match the coil to your needs. I don't believe you hafta go directly from the 'not really all that great' OEM units to the very expensive a/mkt units to do that, there are some pretty good shocks that aren't so expensive. Some are still 'off the Shelf', and I won't go into them, but others may chime in or you can search, but I really like my IKON shocks all round,
and there's an IKON outlet in the USA -
https://ikonsuspensionusa.com/ - You will probably need to contact them tho, I
know they don't list all the shocks they can do or the make/models of machines they can fit their shocks & coils onto, and their rear shocks in particular often aren't in their catalogue/listings, but I'm pretty sure they can do a rear shock for you, with a suitable coil, something that's on a par performance wise but for somewhat less $$ than the more expensive 'big name' a/mkt shocks. You could do a lot worse than checking 'em out.
