A couple things that may help:
First, I didn’t mean to use the Edit Fields menu item that you’re showing. I meant instead to see columns for both the old valued custom field and the new not-yet-valued custom field, sort by the old value, multi-select a matching set of them (up to 50) and change them with direct manipulation (see the outlines below):
Other good ideas are presented in this video by Bastien:
Hope that helps,
Larry