It appears that you cannot do what you want to without some yet-undiscovered hack to the system. Mac OS X seems to require at least one keyboard layout that the system recognizes as a "Latin character" layout to be selected. This prevents your from being unable to enter your password at the login screen, etc. If you selected French, or Canadian, or another keyboard layout that the system recognizes as Latin characters, you can deselect the US layout.
Your problem is that your custom layout, while containing Latin characters, is not recognized by the system as a Latin keyboard layout, and thus cannot be the only selected keyboard layout. See this question (sadly lacking a great answer) for more information.
Note that a great answer to this question would answer your question also. Alas, my answer here only clarifies what the problem is, but I have no step-by-step solution for you. While such a hack may be possible, I see no evidence that anyone has figured out how to convince Mac OS X that a particular custom keyboard is safe to use as the sole selectable keyboard.