@kory, first of all, thank you for your detailed reply!
I must say that originally I wasn’t thinking about expanding the existing background option of the containers. But it sounds great if it is not that complicated to do.
Honestly, I’m not even sure what I was thinking about. Maybe more in the direction of the slider element that was announced a while ago. I think I was discussing it with Alexander during the previous Beta, as a possibility for some of the future updates. It was about some sort of slide-enabled container that would be able to accept any other element on top of it. Those elements (for example headings and text), would slide along with the image beneath them.
I have assumed that the slider image would not be a background-image. So if such element had just one slide, the arrows would be turned off and we would automatically get everything sorted out with SEO: we’d have a proper image below the text.
Such element would also be preferred for the Hero section on pages, because many people love sliders, no matter what some of us think about them. 
I have drifted away from the main topic. From your two proposed options, I think that #1 is risky, because of possible cloaking signals to Google. Serving different content to search engines in never a good thing.
#2 sounds great, but I agree that it might be confusing. I also understand the problem of the lack of proper positioning controls of the image. I believe that lack of repeating options is not an issue, because that is mostly used for decorative stuff. Moving it around might be the problem though. But in the world of html images, there is something much more exciting than the background-position property: Focus point.
Something like this: https://www.jqueryscript.net/layout/Responsive-Image-Cropping-jQuery-FocusPoint.html
Since we have data attributes on images, implementing this is not a big problem. Honestly, I have no idea how heavy and “expensive” a code that provides focus points for images is. I think I have used this only few times really long time ago. But if it is not a big resource hog, perhaps something similar could hit Pro at some point in the future. It would be a very exciting feature.