It would save substantial time to have an efficient method of forcing a WordPress core update to the latest minor version, using the Dashboard so that cPanel or an equivalent isn't needed.
Minor version updates do generally install automatically, so let's assume for this question that they are configured not to (an alternative reason might be that they're failing to install automatically for some reason... bonus points for covering this?).
Does anyone have any methods to do this? I've looked for a plugin to no avail.