Side view cut-away.
If the material has enough give, it should be able to snap-in to the panel, and the button should be able to snap into the bottom of the assembly.
Button assembly for 688-SKPFAA.
I have no clue if this will work, which makes the 10-20 day wait that much more excruciating.
***** Update: Looks pretty good in black detail. Fits in the hole fine, but getting the pushbutton past the tabs will be difficult. I don't like the slope of the cone either, so I'll probably just completely redesign it.
1.852 w x
1.74 d x
0.729 w x
0.685 d x