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You could have a button / hotkey which prompts for a pattern and applies it to both sides. Making it apply as you typed (into the prompt) would be possible via a scripted dialog, but would need more than a simple line or two of code. (We may have a better solution for this in the future, but it's still on the drawing board.)
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I think if you start typing before the folder change happens, it changes the previous folder (or maybe a temporary "empty" file display). There isn't a way around that other than to wait for the folder to load before you start typing.
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I think this can do that:
Or you could use Tools > Find Files > Advanced and enter the names into separate Name clauses (or into one big name clause as (a|b|c...) if it's easier. The latter also works with the Filter Bar.