Often when I am developing something in DEV environment, I find myself checking something on exactly the same page in the Live environment. I do this by going to the URL and editing out the -1.
I do the reverse for getting from Live to DEV, i.e I edit in the -1
I do this both in user mode and in set up mode
How about in DEV where the message/button appears at the top "i xx days LEFT. Promote Development Branch!" adding a Button to the right "Switch to Live", which switches to the same page in Live
Likewise in Live, for those users allowed to do so, add a Button "Switch to DEV", which switches to the same page in DEV.