The "set Do Not Disturb for 12:00AM - 11:59PM" trick has been amazing for me the past month or so I started the experiment. I set it to allow texts and calls from my Favorites through (e.g. wife, mom, dad) -- but essentially every other type of notification is non-urgent and likely even non-important.
By far the best app to silence has been my email. I consider it a luxury that I can come home and not worry about it. I highly suggest it to anyone who thinks they have a screen addiction.
I have my Android set as "Do not Disturb: forever", while allowing calls to still ring. Since people don't call me unless it's something urgentish, it works well, and notifications never distract me when I'm with others any more.
By far the best app to silence has been my email. I consider it a luxury that I can come home and not worry about it. I highly suggest it to anyone who thinks they have a screen addiction.