@OP:
Although I admire your rigorous approach to ensuring nothing can go wrong, I must inform you that the reason is probably, as Hax has hinted at, not an error on your part but the fact that the EB 1 installers do not create proper shortcuts. This is a bug in the installer itself, which unfortunately cannot be solved by rebooting after every screenshot.
Quote Originally Posted by Hax View Post
Right-click on "play EB", then select "properties". It should say "Goal" somewhere. Make sure it looks like this: '"C:/.../Rome - Total War/RTW.exe" -mod:EB"'
“Target”, not “Goal” in case you are confused by not having any such properties...

From looking at the screenshots that shortcut (the EB Play file) should contain:
Target: "C:\Rome - Total War\RomeTW.exe" -mod:eb -show_err
Start In: "C:\Rome - Total War\"

The errors related to “java” suggests a different problem. If you have Java installed you can locate where you have installed it, and then find the folder called “bin” inside this location. It contains the java.exe program. Now modify the validateInstall.bat file to replace its use of “java” with the full path (quoted) to the java.exe program. I.e. modify it to use, for example: "C:\Program Files\Java\jre1_6_21\bin\java.exe" instead of java or java.exe. That should fix the problems provided that (a) you do it right, (b) do not modify anything else in the bat file. So if something originally read “java -jar eb.jar” then you should not touch the “ -jar eb.jar” bit.