I wasn’t able to “level out” the metal button rocking action, as everything I tried under the cap impedes the plunger movement.
But the good news is, I eliminated virtually all rubbing / scraping by polishing both the metal button “tiny lip” & the corresponding surface inside the tail cap (see hash marks on previous pics). When viewed thru a magnifier lens there were machine grooves on both. I used one of my wife’s finger nail tools, that is a softer stick (not metal) with 7 different levels of grit. I used the 3 finest polishing grits, only. Had to cut it up to small thin stripes to reach inside the tail cap, kinda tricky. I lubricated with Vaseline upon assembly.
The not so good news is, I was able to do this delicate work because I have a shop with lathes. But others may be able to achieve this with other methods, ie. Dremel tool with wheels. etc.