Something that bugged me when I ordered, there's really no order status window. I don't know which stage my mattress was on or when it would arrive. I actually didn't know until the day before it arrived that it shipped.
Something as simple the Domino's pizza tracker (order processing, processed, manufacturing, shipping, etc) that shows the status of my order would've been nice. Like you said, proactive status updates, even if it's about delays, put customer minds at ease.
The status tracker could also drive traffic to other informative parts of the site. For instance, you're mattresses are American made. If you source materials from a specific place, outlining where a customer's mattress is coming from could be cool. If you source from multiple American companies and manufacture in multiple locations, a customer could track where their mattress is coming from. I think it would add more weight to the claim of American Made.
I'm very happy with my Ten and have slept soundly since I got it. I'm a fan.