An experiment:
Instead of completely removing the retaining heads, use a Dremmel tool to "slice" off the "mushroomed" portion leaving the stem, aka leaving a shaft, to attach epoxy, something for the epoxy to grab on to.
For "epoxy", consider JB Weld. Use a short section of plastic straw (banned in San Francisco) to form a new "mushroom" head.
Just tossing out some ideas.
Jim