I think the vague times with a more precise tooltip for the exceptions are best for most users...
But if you don't mind seeing the timestamp in the same format as the tooltip, you can use some custom CSS (just create a user stylesheet or userscript to add some custom CSS) to replace the regular timestamp text with the tooltip text.
All of the "vague" timestamps (from what I can tell, there may be some I missed) have a class of either
relativetime-clean and have the full timestamp in the
title attribute. So you can do something like:
font-size: 0 !important; /* this hides the text without hiding the element itself */
content: attr(title); /* this adds the content of the "title" attribute to the element */
font-size: 12px; /* re-set the font size so we can see the text... */
Which gives us this:
It's not perfect (it messes with some font sizes for example), but it's a start.