A dark and weary road could stretch ahead of you! I passed this way about 16 years ago when researching IA routes with an American friend for a VA feature.
I'm not sure that you will find what you want in any one book.
A couple of books that will give you the most information are:
British Airways Vol 1 : 1919-39 The Imperial Years by R.E.G. Davies ( a master of airline histories)
Imperial Airways: The Birth of the British Airlines Industry by Robert Bluffield
A book that details the aircraft of IA is The Imperial Airways Fleet by Stroud
You can get a reprint of the Imperial Airways Pilot's Handbook and General Instructions 1924.
A book that concentrates on the Empire Flying-boats is Adventurous Empires: Story of the Short Empire Flying-boats by Philip E Sims
There is a Haynes Manual for the Empire Flying Boat - it was recently available from The Works
A detailed book on the design and engineering of the Empire Boats is Flying Empires by Brian Cassidy. He made it available as a pdf from his website at one point but I don't know if he or the site are still on the go. Counting rivets, he'll tell you exactly the size and location.
There is a book by Alexander Frater describing his adventures following the old Imperial routes to the East. I recall a tale regarding alternative uses for ping pong balls............ Beyond the Blue Horizon.
Finally there was a paperback about the rescue of an Empire Boat from a stranding on an African river - Corsair? - but I forget the name.
Timetables are available from
www.timetableimages.com - one of the go to aviation history websites.
Abebooks and ebay are your friends, just don't get drawn into paying daft prices! Sadly I have all of these and a couple of pictorial histories that are short on any detail that you may want.
Cheers,
Allan