Blogger doesn't make things easy (all sorts of undeclared and undocumented styling of certain elements), but it does make them do-able. Each blog in the sidebar now shows -- and is sorted by -- the time of its most recent post. This does take away a bit of the site's repose, but convenience carries the day for now.
(Though I was able to massage the extra whitespace out of the BlogList widget, some still remains in the Archive list. If anyone knows what Blogger is covertly styling therein, please email or leave a comment.)