There is no consolidated way to save or export both your button layout and its contents. If I chose to pursue another version, that's actually one of the features I'd classify as higher priority.
Anyway, if both computers are at the same aspect ratio, just mazzify the second computer with the same button layout as the first but uncheck the "place actions in buttons". Then logout and copy the BongosActionBar.lua settings file from one character's savedvariables folder to the other.
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