Clamp the cam arm in the vice horizontally, and file off about half of the metal from the raised portion of the armature. All the metal filings will be kept from getting inside the ZIF socket this way.

In this side view of the filed-down armature it's easy to see the important reduction in height which has occured. Before tweaking the raised portion of the armature stuck up higher then the silicon die, preventing proper heatsink seating. It now lies just slightly above the surface of the processor PCB. Easy tweak if there ever was one.

A.1) Cam Box Avoidence.

I really don't see an easy way of getting around the cam-box of the socket-370 with out totally messing up the socket. Thankfully most heatsinks do not overhang this area of the socket so it isn't really much of a problem. But if your heatsink does, I think the easiest thing to do would be file away the heatsink base.

In such a case, about 0.5mm of material from the base of the heatsink would need to be removed (if it overhangs the cam-box on the slocket). Anyhow I found these CAD drawing of the socket and FC-PGA chip so the dimensions tell exactly how much material may need to be removed.