The Elamite World seems pretty exhaustive, I suppose, but even trying to skim that book for qualitative information that teaches me (a layman) more about Elam makes my head explode.
I realize that there are linguistic and evidence-based barriers to getting a good picture of Elamite life. Despite this, the few things we've found (e.g., the significance of the names of their gods, their population and settlement pattern over time, their clear differences when compared to Mesopotamia, their possible similarity to other cultures who lived in similar conditions) should give us some kind of a broad-spectrum view of what the Elamite experience may have been like, right? Is there any work out there that tries to tackle the Elamites from a broad, layman-friendly perspective?
I'm afraid you'll have a bit of trouble with this one. The Elamites aren't really a layman-friendly topic. There's just not enough popular interest in it to produce any pop histories, or even really narrative monograph books that would be a bit more accessible. It certainly doesn't do you any favors that most of the scholarship on Elam is produced in French. If you can read French, that will open a few doors for you on this subject (and most ancient topics really).
The most lay-friendly resource I can think of for you is Encylopaedia Iranica. Most of the articles are digital now and free to access at that link. There, you can find encyclopedic coverage of basically every topic in Iranian history, including the Elamites. You can start with this page on Elam, and work out with search terms from the articles you find there.
You're absolutely right that The Elamite World is an overwhelming book. Other options I can recommend that won't be less scholarly, but might be less daunting are: