Nice try, but no cigar...

問題

Home button apparently stuck down or otherwise non-functional.

修理

Repair was as advertised; heat gun + suction cup and spudger (along with a thin guitar pick to keep things apart) worked fine to get the screen away from the back case.

Replacement home button however should have adhesive around the edge so that when placed in position it stays put. Mine didn't.

Turns out the problem is not the button but the dome switch under the button, so I've ordered that part off eBay and will try again. I kept the original home button b/c it still has some "stick" to it but I may resort to others' suggestions for applying spray adhesive on a toothpick to the new button.

アドバイス

For others in this situation: once you have the screen up and before you remove the home button, try the dome switch using the spudger or a pencil eraser; if it's not working you won't want to remove the button until the switch has been replaced—it may be OK as-is.