I want to consider what you say but I don't understand.
I see six support arms if we're talking about the same thing. Each pair forms a triangle with the screw as the base.
I'll call the three pieces that are free to pivot fingers. The bottom step of each finger appears to be 3" long.
The inverted piston would be like a coffee can but bigger. The ring would start out lying on the rim. The tool would be lowered (knob end up) until the fingers extended about 3" into the piston so that the short second step of each finger would be in the piston ring.
Then the tool would be expanded, pressing the long steps of the fingers against the inside of the skirt. That would prevent them from pivoting, and the second steps would expand the ring enough to tap it carefully down onto the outside of the piston.
It looks stable to me.