Page Editor: Can we tell widgets to ignore certain pages in a node/app?

I have a widget that I’ve added to the top of the page when browsing a ‘wiki’ style pages database. It looks good on the node’s landing page like this…

But it gets in the way on all other pages to do with this node, such as page records:

Is there a way I can tell this top widget to only appear on the [domain]/wiki/ landing page of the node, and not in any other areas of that app? Is it something I can make disappear with custom CSS class/IDs, or something that needs to be added as a specific Page Editor option?

Also while I’m here… it’s still a bit weird that you can’t add “top of the page” widgets underneath the page/app title block (as in the first image; the ‘Featured Records’ block cannot be placed between the ‘Sonic Wiki’ title block and the ‘Categories’ block). It’s something that always struck me as odd in V4, can it be something that can be resolved in V5 I wonder (not necessarily for 5.0, but later down the line)?

Edited August 9Aug 9 by Dreadknux