You will need to make the folders all the same names as previous editions though for steam to make it work... I had hoped you could click on the file and just download it all.
Don't leave CIV4 just because of this stupid update, it is a great game hence why we are still playing near 10 years on now, and you have just set up a few cracking games. Once it is all settled down it will be as if nothing changed. It is only because modified assets are locked anyway - otherwise there would be no compatibility issues between the versions
I am not going to be with fast internet for a while but I could try and convert it to a single zip file that would be downloadable in one go, that would certainly be easier to set up. Might be a while before I am able to upload it though. Also below are the only changes needed to make sure pitboss still works, these might be enough to make the PBEM games work too.
I was able to restore DirectIp functionality in BtS for both the game and the PitBoss server following GermanJojo's post with some differences:
1) Turn off auto-updates for Civ4 on Steam (Library-> right click on Civ 4 BtS -> Properties -> Updates -> Do not automatically update this game).
2) Close Steam.
3) Replaced following files from a not up to date version:
C:\Program Files (x86)\Steam\steamapps\common\Sid Meier's Civilization IV Beyond the Sword\Beyond the Sword\Civ4BeyondSword.exe
(MD5: 8e7bccc61849d684bfbba44e9c9bc647 - SHA1: 541f9b20da74d2a94dc1d9b49bb9dd8116e6c72e)
C:\Program Files (x86)\Steam\steamapps\common\Sid Meier's Civilization IV Beyond the Sword\Beyond the Sword\Civ4BeyondSword_PitBoss.exe
(MD5: 018697e7197ae214e7ca7da3093f58e5 - SHA1: af5805d237430e8891cd34b1d94985222f4dd7a2)
C:\Program Files (x86)\Steam\steamapps\common\Sid Meier's Civilization IV Beyond the Sword\Beyond the Sword\Assets\Python\PitBoss\PbWizard.py
(MD5: 0537702ddbbb4649914db16e166894e6 - SHA1: 628968016d4ce29c0b0cd969888e3b7026ec641f)
(It was not necessary to replace CvGameCoreDLL.dll.)
4) Restart Steam and load the game.
As reference my platform is Windows 7 x64.
Be careful to don't mix Vanilla/Warlords/BtS files while you replace them.