Is there any way to prevent Battle.net from locking an account while traveling
Do you have a smart phone? Blizzard has an authentication app that lets you "validate" who you are.
It sounds like there is ghosting software as soon as you log off, but you have access to "install" applications when you are using it. You mention that you're downloading it every time. Why don't you copy the Starcraft 2 folder to a USB stick and then just copy it to the computer every time you are on it?
Starcraft 2 doesn't need to be installed in the traditional sense as you can just copy the folder to whatever computer you are using it on and just run the application.
The answer truly is to give support a call. The fact of the matter is, this kind of DRM is only in place as a blind default - good customer service representatives will take your convenience and patience as a customer into consideration far above strict adherence to the rules. They value you as a customer. Companies have learned a lot since the famous Spore DRM fiasco that Electronic Arts pulled so many years ago already. This kind of failure has changed the industry for the better, and Blizzard is already quite good with their customer service. In short - just talk to a real human being, and they should put a stop to this kind of issue.
If the app becomes a pain to use or you want to make it easier, you might want to take it up with Blizzard. As Southpaw said, real humans are more patient and the company knows more than us. Some technical features of an account (like overriding that lock) might exist if you ask them.