Alright, I have spent quite a bit of time on trying to figure out a non-root solution for this. And I've tried pretty much everything I've seen suggested: Silent mode, quite mode, a variety of methods on the apps Tasker & Trigger, the stock charger, a variety of USB chargers of different, and even tried enabling and disabling a few different settings (Including the QuickCircle setting, which someone suggested).
The only thing that has worked for me thus far is a bit of a compromise, but one I'm willing to take for a good night's sleep (excluding just giving up charghing my phone at night on my side table or giving up the phone).
Change Settings > Sound > Volumes > Notification Sound to OFF or low
AND
Change Settings > Sound > Vibrate Strength > Notification to 0 or low
This will not turn of the notification light or stop the screen from lighting up (I just turn my phone screen side down at night). Quiet Mode does NOT have these options available to change, so that's not an option. And keep in mind, this will affect all Notifications, including texts or e-mails. That doesn't bother me too much, because I glance at my phone screen enough times a day or am not even around my phone to hear it anyways. Another option would be to change these settings right before you go to bed and again when you wake up -- but that's too much of a pain for me to remember.
Personally, I keep my Notification Volume at 0 and my Vibrate Strength to around 30-40%, and rest my phone on a cushiony towel at night. Doesn't wake me up at all, and I'm not exactly a light sleeper.
It would be pretty sweet if Trigger had an LG plugin for this sometime down the road, although I'm not sure if that will still require a root or not.