On every page, that sounds like an awful lot of work; on the very busy pages, that sounds like it could be useful. I'd agree with the ordered archives being the "archives of record," more or less (less refactoring = more authentic, if perhaps a little less useful).
As far as linking back and forth, I think all you'd need would be a template with two parameters: the section name and archive page to be linked to. Example:
{{X|Arbitrary section|Archive 4}} -- links to [[Talk:Page/Archive 4#Arbitrary section]] {{X|Arbitrary section|Foo discussion}} -- links to [[Talk:Page/Foo discussion#Arbitrary section]]
The template itself would be pretty simple, too:
See this topic in [[{{TALKSPACE}}:{{BASEPAGENAME}}/{{{2}}}#{{{1}}}|{{{2}}}]].
..or some such. I haven't tested that, but obviously something along those lines should work.
Just slip that template in, directly under each section heading, and you're set. Do something to set it apart from the rest of the text -- I'd say bolded and smaller font should be fine.
It occurs to me that it might make more sense to have the archive name as the first parameter, and the section name as the second -- it's all the same to me, but if anybody cares and this template gets made, speak up quick. ;)
Just a thought. This is feasible. Is it desirable? -Luna