The spring cup/apparatus is an (almost) interference fit. Just push harder. Then you simply twist the bendix to push everything back down.
I have replaced the GG circular spring with the Honda spring, but I haven't had the gumption to remove the hog ring from the shaft to change the gear or inner spring. I believe the inner coil spring (inside the cups) is the key to the whole operation. That lighter spring allows the gears to more easily interact, and then prevents the gears from disengaging too early.