I've got the re-coil top off motor. There appears to be
a label over the re-coil pulley, which spins in this shroud one
way, and creates tension in the spring when spun the other.
Question:- How do I get the damn thing off?
Take it to a mower mechanic. If you know what to do pull cords are quite simple and only takes 10 minutes, so it is quite cheap to get done. Pull cords I have done in the past simply needed the knot to be undone. Cord replced and about three turns of pretension put on the spring. You need to ensure that you get the correct length and diameter cord.