Successfully fitted the J3 to my chair.
This wasn't in fact difficult:
Unvelcro existing sling back - this was actually one of the least easy bits as I wasn't entirely sure where and how it connected under the seat, in the end it unvelcroed itself and fell off in my hand.
Unvelcro tension straps.
Unfasten extension tubes and push handles - I didn't actually realise the chair had extension tubes on the back uprights until I got the tension straps off. In retrospect the top of the tube being a different colour to the bottom was a bit of a clue.
Install clamps for J3.
Drop J3 in place.
After taking it up and down the street I decided I wanted it a bit higher, so reinstalled the extension tubes and push handles and clamped it onto those instead.
An unexpected bonus is the back will still fold without needing me to disconnect the J3 (which only takes a couple of seconds anyway), and in fact the J3 makes it easier to see if it has unlatched properly.
Looking at it now, it's giving me an additional two or three inches of support up my spine I didn't previously have, plus a noticeable amount of lateral support that I didn't have at all. I may possibly want to shift it back, or angle it back slightly, but those are slightly more involved, so I'll give it a day or two before I try that.