It's looking good! Unfortunately, there's more change required that just a CSS centering for the mobile display, since the scrolling somehow sets the page at the top after every image-update.
It's going to be easier to simply hide that display for mobile devices by editing your /includes/templates/responsive_classic/jscript/jscript_responsive_framework.php, adding the following to the mobile-device clause:
Code:
$('#whatsnewscrolling).css({ 'display': 'none', 'visibility': 'hidden' });
P.S. You're letting yourself in for a "world of hurt" by directly modifying the responsive_classic files, since you'll need to merge any updates in with your changes from the get-go on the next Zen Cart update. Better to use the Clone a Template plugin, clone what you've currently got for the responsive_classic and then make further edits on your cloned version.