Not sure if you’re aware of this, but there is an option for that kind of tucked away inside the Dev Toolkit.
Just pop it open, click the Tools tab, and scroll down to the very bottom for “Copy Element” and “Paste Element” (in my screenshot below, I have an element named “Body” selected).
I may be mis-remembering, but I believe one caveat is that when copy/pasting across sites, your Globals (colors, etc.) may be different – and this copy/pasting doesn’t do anything to map the values to the “new” site. So I believe you can end up with duplicate colors, and may need to do some cleanup work. But overall, big time saver.