from the original post:
"(The W10 taskbar clock shows two lines on my machine. No other software for this, just W10. The parameters are customized in Control Panel > Clock, Language, Region.)" ...

If you WANT the year in the notification area date this thread isn't relevant to you.
If you don't want a year in the file explorer date this thread isn't relevant to you.
If you want NO year in...

No one, not even Vishal Gupta, could help me with this. I finally had to use a workaround, it just ain't in Win10 settings or approachable (that I could find) with a hack.

I ended up using...

Running Windows 10 fully updated. My File Explorer windows show several columns in the Details View: the Filename, Date Modified, Date Created, etc. The Date is formatted like this: Day Month Date...