Interesting… Not making promises here, but I am off-and-on thinking about this.
Is there a specific key, meta-tag, or something like that dlvrit is looking at to decide which image to post to Insta? Because if there is not, it would be hard to present the correct image…
Then, when we have that, we could generate a square image based on the available data; this would not 100% be identical to the current social-image, as — of course — there would be a different section of the background image shown (the center square would probably be used).
Placing logo and text should not be a problem.
The only difficulty I see here would be that you would have to choose an image that is suitable for both the 1200×630 format as well as the 1080×1080 …
Again, no promises, but perhaps we could make an add-on for this …