I got here by accident actually, as I was looking for a way to get the clock to stop flashing every time the phone moves. But I have a legit fix for anyone else that makes it here.
For anybody who doesn't want to read all the threads and scrolls to the bottom like me, you turn it off by going into your little moto app (found on my phone by searching the apps), and turn off all the display functions.
Once you've turned off the clock from flashing every time the phone is moved, if you want to still keep all your notifications you just go into your settings (the app with the cog symbol), then "Sound and notification", and scroll down to "Notification". There is two options here, one for when the device is locked, and the other is app notifications.
If you change the "when device is locked" to the option "hide sensitive notification content" it will just tell you that you have a notification from whatever app is sending it, but give you no content.
To be explicit, the notifications are shown on your lock screen but no information is given about the content, just which app is notifying you. The other two options basically are "all" and "none"... I think you can all work out what they do.
You can set some apps to not notify you at all if you're getting too many, or to notify you even if your phone is in "do not disturb" mode through the "app notification" setting.
This specifically will make it so that your phone has notifications on the lock screen when you push the power button, and have the clock stop flashing at you every time the phone moves. The phone won't flash on and show a notification as they appear though with this method, for that you need either to live with the moto screen or third party apps.
Sorry this is a long explanation but hopefully this fixes the problem for anyone who's made it here, without needing 3rd party apps necessarily, any serious technical knowledge, or tearing out any hair
I hope this helps!!