I've now moved a few things around on the homepage and on the category pages (dated archives and individual pages are to follow). Much of the same functionality is there (some links were removed), but it's now in a different order and hopefully will look a little cleaner. Much of the change was behind the scenes, i.e. elements that appeared on different types of pages are now included as a template in their own right (so if I edit them once they edit everywhere).
This makes the master templates a little easier to read!
Looking at it as a whole, I don't think many people would consciously notice the change - but the sidebar in particular seems to flow a lot better now.
Having tidied, the only way to drastically reduce the sidebar is to remove many of the 'recent post' links - this would remove a large amount of functionality for me and so I don't think I can take that step.