If someone else comes across this post, I figured out a brute force solution.
When the importer is running, it imports posts from Tumblr starting with the most recent and working backward chronologically. So I decided I would let it import posts until it got to the point where it caught up with the posts I already had in my WordPress blog.
To force the import to stop, I cleared my data right when the import was at the point I needed it to stop. The option to clear data and abort the import is found in the plugin page in the WordPress admin area.
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This reply was modified 1 year ago by goodolvic.