One approach:
Outline view in Word lets you reorganize your entire paper by dragging
the headings around. So if you show only the headings, and then sort the
headings, then all the text under each heading will stay with the
heading, but the headings will sort in order.
So to do this, you will need to apply Word's built-in Heading 1 to your
page titles, if you haven't already.
If you don't like how Heading 1 looks, you can change it:
http://shaunakelly.com/word/styles/ModifyAStyle.html
If you have already formatted all your chapter titles, say, as 14pt
bold, you could use Find and Replace to find all text that is 14pt bold
and format it as Heading 1, rather than doing it manually.
Then View | Outline, click on the 1 on the toolbar to only show the
headings, select all, and use Table | Sort. I would MAKE A COPY before
doing the sort--I have only ever tested this with about 10 lines of
text, not a 365 page book.
More on Outline View:
http://word.mvps.org/faqs/formatting/usingolview.htm
Applying Heading 1 to your page titles will also make it easy to create
your table of contents:
http://shaunakelly.com/word/toc/CreateATOC.html
More on using Word's built-in headings:
http://shaunakelly.com/word/numbering/UseBuiltInHeadingStyles.html
Side note: I find it odd that alphabetical is the best way to present a
*book*. I suppose if it's some sort of manual. It sounds like it might
be disjointed for the reader.