Maybe I'm not understanding, but I thought a modal login would behave like this site (using a different login plugin): fashioncow.
There is a login link, and no form displayed. When you hit the link, you get a css-styled pop-up with the form. It never leaves the page its on.
Can I get Login With Ajax to do that? On my new site, when I set LWA to use the 'modal' template, there is no change, and the form is on the page.