It can be done with some CSS. This is the initial CSS to do it in css_additional.css. This will relocate the login to a static location on the channel tabbar, adjust top and right as necesary. Making it responsive will require more work. Javascript may be a better alternative.
Code:
.secondary-nav.h-right {
display: block;
position: absolute;
right: 5em;
top: 332px;
visibility: visible;
}
#main-navbar-wrapper {
visibility: hidden;
}