I tried this last week, though I haven't driven the route I made.
I downloaded the google maps app
Once I signed in I was able to see all my created maps. (I think it's called My Places when you're on the google maps website).
That was exactly what I was looking for.
BUT I am looking at it now and it's a little more confusing. I think I can find it by clicking on the person icon in the upper right.
Then the settings icon upper right
Then Maps History seems to not only have the history of what I've asked it to map in the last few days on the phone, but I can see some of the My Places in there too. They have different icons.
It's not a very intuitive interface compared to Waze or Apple Maps. I found Friday that it was .5 miles off for a place I was going. I had been there before though, but if I was in an unfamiliar place it wouldn't be good. I don't like the voice as much and find that while it lowers the volume of my music, the voice volume is not as high as Apple Maps or Waze, making it hard to hear. I also like how Waze and Maps show more data on the screen and with Google, you have to toggle through arrival time/minutes remaining/miles remaining.
Can you run two programs at the same time? I can try that and see how they compare. I'll need to map a route for a trip I'm taking this summer so I really hope it works.
Let me know if you can see your maps in the history. I signed into my google account as soon as I opened the app, maybe you didn't?