Found A Fix!
I don't know why this worked, but it did, and I'm not planning on figuring out why.
I spread the largest game files out onto multiple disks using symbolic links* and I set the compatibility mode to windows server 2003 (this is not what fixed it, but improves performance when there are a lot of threads)
and suddenly the game did run in exclusive fullscreen mode
*a sombolic link, for those who do not know, is a link to a file or folder which, if looked at from the perspective of a program like a game, looks like a normal file and it will not notice it is in another place.
- you will need 2 extra folder (preferably on an extra drive for improved performance) to store the game files.
- open the game folder and your 2 extra folders. (right click on game icon and select 'open containing folder' when using steam, right click the steam icon and open steamapps > common > tomb raider (or something)
- Move bigfile.000.tiger and bigfile.003.tiger to one of your extra folders and patch.000.tiger (if you've got this files) to your second extra folder. (if you don't have this file you wont need the second extra folder.)
- open cmd by going to your start menu and searching for cmd, right click it and select 'run as administrator' (with the shield icon)
- type cd /d [path to game folder] (you can find this by clicking in the empty space of the address bar of in the windows explorer window)
C:\user\peter>cd /d C:\Games\Tomb Raider
- type mklink bigfile.000.tiger [path to extra folder]\bigfile.000.tiger
and repeat this with all files, patch.000.tiger goes into your second extra folder.
D:\games\Tomb Rader 2013>mklink "E:\extrafolder\bigfile.000.tiger" bigfile.000.tiger
after that, you can close your game folders and the ugly command prompt cmd window and play the game.
hope that helped! enjoy your game!