I don't see an obvious way to avoid repetition when importing to a field with logging enabled, other than not importing into that field. But then new records would be missing that field.
A suggestion is to import into that field, causing repetition, but then hide that field from most reports and forms, and instead use a formula text field to extract out the most current data. Then provide an alternate form for users to use (accessed by a URL formula button) to display those raw fields with the logging. So users would only use that alternate form if they needed to see the update history in that field.