Built this; it's in review as https://github.com/gulkily/v3/pull/26 and not live until it's merged and deployed.
After Check for updates, the Deploy page gets an Incoming row: commit count and size (files changed, lines added and removed), then the commits newest first with author and date, up to 20, each hash linking to GitHub. If the update also touches a file the server keeps a local edit to, like public/.htaccess, the row names it, since that's when a deploy can stop on a conflict.
The queued button is now "Queue deploy". When you press it, the status line says it usually starts within a minute, then counts how long it has been waiting for the task worker.
Two calls you might want different: merge commits are left out of the list (they repeat their branch's commits, so the Behind count can be higher than the list), and the list folds up under its summary when it's longer than five so the buttons stay near the top on a phone.
./v3 deploy --status prints the same thing as Incoming-* lines.