That logic related to home/front page in core is a horrific mess and very special snowflake. You absolutely don’t want to repurpose any of that.
It wouldn’t be that hard to build what you want in custom site:
- Have your videos page designated somehow (easiest way is by slug, but be careful of slug getting changed, clients like to mess with those)
- Detect the page by your criteria in editor and display notice you want
- In your archive template retrieve the page by your criteria and use its ID to retrieve and display content as needed