don't pedal backwards...
Join Date: Jul 2005
Bikes: Surly Long Haul Trucker set up for commuting and loaded touring, old Sekine road frame converted to fixed-gear, various beaters and weird bikes, waiting on the frame for my Surly Big Dummy build
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Without knowing anything about that exact chain, I think you analysis is probably right on. Mushrooming the rivet heads would make for a chain that is less likely to come apart, but it would also take more force to press a rivet out. I bet you can break it with a normal chain tool, but I wouldn't try to reassemble it using the pin you pressed out since the flange is almost certainly shot. This sounds like a perfect time to use a master link.
Given how much of a pain that sounds like, why not just scare up some kind of normal chain that can be cut and reassambled without worrying about mushroomed heads and stuff?