I finally fixed up my "last modified' move code (among other modifications to my UI) and I just uploaded a screenshot here: commons:File:Stripped MediaWiki interface.png. I think in addition to putting the timestamp above the tabs, it'd also be nice to re-evaluate the other "personal tools" links (language, necessity, etc.).
In general, this idea seems pretty easy to implement. Is there any holdup to doing this as a gadget or something now? The only other consideration was whether a more sane output format could be specified in the HTML output rather than trying to parse the lastmod MediaWiki message/timestamp formatting. Maybe a wgVariable has the timestamp of the most recent action to the page? Or one could be added? That'd be so much cleaner for date calculation.
I think the only holdup is features devs being busy with work on stuff like New Page Triage (being previewed this week) and the usual stuff like code review. I agree it's something that should be tested sooner rather than later, and it's totally possible for myself, Maryana, and a data analyst to help push it forward as part of our experiments work even though we haven't hired our first devs.
If this is something you could help us code up, let's talk. If not, then we can at least list out of the order of operations a little better, since testing it for current editors, new editors, or readers each might require a different approach to implementation.