Hopefully I didn't reply to this in another thread. Not that I haven't done that before but I'm positive I wrote a reply.
Anyway you're probably not going to like my reply. You mention 3rd party apps, well my suggestions are based around 3rd party apps. First, I was thinking of changing your launcher. Launchers like Nova and others offer several different options that native ones don't and they also offer customizations that users often cannot find natively.
If you had a Samsung I would recommend Good Lock which has an addon called Lockstar that offers lock screen options that customizations. I don't know if Samsung offers this for other manufacturer's devices but you could look on the Play Store. You'd have to get Good Lock, then add the addon, Lockstar and look through the options.
Finally there's are apps that can send you notifications or generate them. The fist that comes to mind is one that I use called Tasker but it will matter how important this is for you. Tasker is a paid app that also requires some learning. It can do a wide variety of things far beyond this so I wouldn't recommend it if you only plan to this one thing but there are several others, some that are free on the Play Store. I don't believe any are as powerful as Tasker but they might offer some simple tasks that can push notifications. You'll have to test and do some trial and error to figure out if one of them can help.
One thing that just occurred to me is looking up Google Dialer anyway. I know you say that your device came with it but I remember a time when I had a pre-installed app that I found another version of on the Play Store. Same app but one was the manufacturer's offering and differed somehow from the Play Store version. Like they tweaked it for their device...? Beyond that, unless someone else has suggestions I'm about tapped. It's just odd that it would work for someone installing the app but not for someone who's device came with it. Also odd that it a device wouldn't do it natively. That seems like exactly the type of thing someone would use AOD for. Oh and just because that was what I found, I would do my own searches. I stopped after finding one that appeared to have an answer. I'm sure there are more.