So are you saying that 5040x1050 doesn't even show up in the in-game video options menu? If that's true it's not a good sign. :(
If you care to try some testing of surround resolutions (assuming you can find a method that works)
I don't see why it wouldn't work I mean my friend WAS indeed running it with TH2G a year+ ago. Resolutions seem to be propagating dynamically on my system. It is limited to 1024x768 though. That means no 720p (1280x720 is lower than 768 on the vertical axis)
There are 4 methods, one of them is sure to work unless the aspect ratio has gotten locked (which would be a real shame, and I would actually be talking to some of my friends in high places if that is the case..)
Native fullscreen + in game resolution options
Native fullscreen + config options (cfg located in "C:Documents and SettingsDaFoxMy DocumentsStarCraft II BetaVariables.txt" on windows XP the width and height values are the ones that you are looking for)
Windowed fullscreen (This simply locks to your desktop resolution, Great feature that was first used in the Source Engine I believe. It allows you to alt tab without removing the game from [video] memory, which saves upto 10-15 seconds on each alt tab)
Windowed (In game resolution options work I believe, you can also dynamically resize the window, there is also a separate entry for windowheight & windowwidth in the config file)
I must say they put quite abit of time and thought into these options.