It seems everyone's resolve for layout panel sliders not working in the template manager is done offline. There is a SOLVED for one after an update but I don't see what that resolve was.
My issue is a little different. My client had a terribly old Joomla site at the root. In a folder at the root I developed a brand new site using the gantry rocket launcher of just the gantry framework and the latest Joomla 3.2.1 right from the start, no updating of any sort. The developed site worked great front side and back side.
I completely deleted the old site and moved the wonderfully new site to the root, refreshed the page and was shown a white screen. I called the host provider but the they couldn't fix it immediately so they restored the entire site to their latest copy and would move it for me later. One resolve on their part was to rename a cache folder at the root.
They did later make the move for me and the front side works great and the back side too with one exception: the template layout sliders don't work.
One thing I did do before attempting the move was to make an Akeeba backup of the new site. I've not tried to use kickstart to restore the site at the root level. I thought I would post here before trying that.
I would suggest you to try to remove Gantry completely, clear all the cache you have enabled and install Gantry from the beginning. The same applies to the template itself
Well, I would say this is now SOLVED. I wasn't able to jump in and do what Igor suggested due to time constraints. But I came back to this the other day and followed up with the Gantry updates that were waiting for me to update. I discovered that the template layout panels are ok now. All is good.