Iain,
I'm really unsure what's coming together to make your SCLogin module not play nice. The bottom:inherit setting seems to be causing more issues than it's worth.
If you update that CSS to the following, the login area will show. It should be necessary to set the height, and there are still some CSS issues, but try this out and it should be usable. Then, let me know any other fixes you'd like to implement:
div#login-modal {
bottom: initial;
height: 325px;
}
I hope that helps!
Alex