Thanks for the test account. That helps a lot.
For making the button smaller, you can use the following CSS:
#scLogoutButton .btn.btn-primary {
height: 25px;
padding-top: 2px;
}
As for going to the right, I'm not sure it can go any further right. It's already in the right-most position of the .rt-flex-container which is in your header. Where were you looking to put it?
Thanks,
Alex