If you are only using “a feature” of one theme, you may be better off taking your “standard” theme (the one you’d like to use throughout) and then taking the functionality from the “one-off” theme and adding it onto the former.
This goes in-part with the fundamental idea of not adding such functionality to a theme – it would be better suited for a plugin instead. That way, it’s portable. Right now, you’re facing a dilemma which could have been rectified by making that functionality portable.
I’d go back to the developer to ask them what’s involved in making it into a plugin (it’s not just going to be copy/paste).