I had an ugly accident with my iPhone 6 Plus. I fell scratching the pavement with my iPhone 6 Plus on hand (yeah my hand suffered from this accident too). Yep, broken glass all the way through the LCD.
It when smoothly with the iOpener tool as part of my tool assets.
Go with the iOpener tool to reheat and peel off any adhesive. Specially the ones from the home button and the home button cable.
I've broke a tiny cable while I was trying to peel off the home button cable (step 32 of iPhone 6 Plus Front Panel Replacement). That's why I had to get the shield plate to get the home button cable (it comes glued the shield plate).