Micheal H. Huge, thanks for that, inspired by your post - tentatively I'll say that I think its now fixed. but perhaps not quite as simple as you suggested!
I say tentatively, because I remember that I had the setup described below back in version 1.5-2.2(ish) when I made the current version of the site and after a few days I found that it didn't work... but I can't remember why. Which was why, having tried several alternatives, I ended up with the weird set-up described in OP.
I'll describe what I have done (and seems to work now) for future reference:
My WordPress address (URL) is http://ministryofmanipulation.com/wordpress (to match the install directory)
My Blog address (URL) is now (at your suggestion): http://ministryofmanipulation.com
Although I actually want my blog to appear at "http://ministryofmanipulation.com/blog/"
Because it was historically located there with an alternative static front page at root.
(aside:I'm not 100% convinced that I want the blog appearing at the root url long term. I know that in the short term this creates a slightly bum set-up where my blog is at "/blog/" and "/index.php" but I'll deal with fixing that headache later!)
But I'm running as a small CMS and have 50 or so static pages, which I want to be at URL "/pagename" (which they were, and still are with the change in blog address - good so far).
By removing the "/blog" from the blog url, as you suggested, all my posts move from "/blog/postname/" to "/postname/". Not good, lost all my old links. So to fix that, I have also adjusted permalinks - custom name to "/blog/%postname%/" (previously just "/%postname%/")
same with category base now "/blog/category" (previously just "/category")
Now I'm missing one important page "/blog/" ! which is where most of my visitors bookmarks bring them.
I solved this easily before, by having a blog PAGE called "Blog" with no content in the page, but with its own page template to make it look like a blog page. with that (www.ministryofmanipulation.com/blog/) looks identical to (www.ministryofmanipulation.com/index.php)
Ta da, that appears to have put everything back in place, and fixed the original problem.
(aside: I had unsucessfully tried to solve this last item by adding a line in htaccess:
Redirect permanent /blog http://ministryofmanipulation.com/index.php
Which of course breaks the URL link to every blog page by removing "/blog" from it, Doh.
I'm sure that if I understood rewrite rules a bit more I could have cleverized this, but no worries, above works ok.)
So, my whole site is at the same urls it was before, and this has solved the original problem with the admin manage posts link. Thanks again for the suggestion.
It's not perfect, I need to decide where the blog should be. and then I'll settle on one of those locations.
But first I'll solve some more important "wp_post2cat" problems that have arisen with 2.3 :(