It is a strong spring, but it's perfectly feasible to compress it again to re-assemble it. It's important that (as you say) you screw the pushrod IN and not out to dismantle it. I have dismantled mine a couple of times when I've changed the bearings in the clutch – it made a racket when disengaged.
You need to have the push-rod and ball bearing assembled in place on the clutch operating shaft, press hard down on the driving plate and whilst it's pushed in, insert a smallish screwdriver (biggest you can get into the hole!), and rotate the push rod anti-clockwise to screw it into the drive plate. Make sure you engage at least a couple of threads before you stop pushing. A smear of grease on the threads beforehand may help.
If you aren't strongish in the hands or suffer from arthritis or something, you may need to scheme out some kind of tool to compress the spring to re-assemble. I believe Myford of Nottingham had such a device, but I've no idea what it looks like. I guess it may have been some sort of device which fitted to the right hand end of the clutch assembly, presumably with the clutch operating arm removed.
Get a 5/32" ball before you start, and then when the original one pings off and disappears, you can fit the spare.