...sending them to Steve Young
...desoldering the entire bakelite plate from the machine
...driving myself nuts using inappropriate tools

I could drop silver solder on it for a temporary-ish fix.
I could make a duplicate part with a laser cutter, skip the riveting business, and just epoxy everything.
I could stare at the bad rivets intensely and hope my telekinetic powers would reshape them.

But really I just want the easy fix: Drill the bad one out, snap the new one in.

Where can I find a dad gum rassen-frassen tool to do this?

Found something promising... http://www.hansonrivet.com/hand-rivet-squeezers.htm

Or this... http://tubularrivetclincher.yolasite.com

EDIT: Don't order this. It doesn't stay aligned throughout the riveting procedure.

I bought one of those. Didn't work. The cup does not secure the rivet flush against targets, bakelite, etc. and allows too much lateral movement. Only pressure applied with a rivet die set will provide a smooth, secure fit.

Searching for pinball rivet stepper Gottlieb etc. on Pinside (and indeed, the internet itself) does not seem to turn up anything terribly useful regarding the specific replacement of EM stepper rivets.

Aside from the hand rivet squeezer and clamp-style custom clincher above, I am investigating a third option: Stainless steel tack screws. They also have smooth oval heads and can be easily attached via a small nut on the back. Assuming the gap isn't too narrow between adjacent rivets it could be a simple matter to install one. Might be a good fix for those without the determination to do a partial or full re-rivet.

Tried the Tonka clamp riveter. No good. The dies do not remain aligned throughout the process. Pretty much useless.

Solution: We modified an arbor press using some of Pinrestore's kit materials along with a custom aluminum strike plate. Works very well. Target and stepper rivets now bend to my will.

Replacing rivets is a time-consuming process: Unsolder the stepper disc, remove all wires (and carefully note their position), drill out each rivet, clinch new ones (ideally w/new solder lugs), resolder all wires, and resolder disc to the machine. However, once done, it sure is nice knowing those connections will be SOLID for years to come with no more flakiness.

Time to get on with some serious riveting...