> users are greeted by what I call Z-Index Warfare
Nice term!
> Or better yet, inject the newsletter signup as a styled, non-intrusive div between paragraphs 4 and 5. If the user has scrolled that far, they are engaged.
They're engaged with the content! There is no way to make some irrelevant signup "non-intrusive". It's similar to links to unrelated articles - do you want users to actually read the article or jump around reading headlines?
Z-index warfare is so stupid (the practice, not the name). It's not only with media publications, but ecommerce sites as well.
There have been countless businesses that have lost out on my money because I clicked on their ad (good job!), start reading the product info on their website as it loads (that's basically a sale), and then the page finished loading with a barrage of popups for cookie consent, newsletter signup for a discount code, special offers, special sale, spin the wheel for a prize, etc. That's when I close the tab and forget about it.