When I switch to Twenty Thirteen, the abilities are different (of course) but the same basic thing happens. I activate the Custom Sidebars plugin, make some custom sidebars, allow the main widget area sidebar to be replaced and replace it in the page. When update and open the page, it’s still the same sidebar as the general ‘main sidebar’.
I am running everything offline using bitnami right now so am not sure how I can give you a link to see the page….I can try to upload it to run on one of my sites unless there is another option you can think of?
Thank you