However, for some small testing scenarios, demos and also some coding fun, I decided to add ChangeFeed support to the Azure CosmosDB data migration tool (link to original version).
So with this special version of the Azure CosmosDB Data Migration Tool you have additional options for the DocumentDB-Source available unter „Advanced Options“:
You can select where you want start reading from the change feed. Either start at the creation time of the collection or select a specific date. I admit I could have added a DateTime-Picker :-P.
At „File to read/store continuation tokens“ you can provide a file name to store the continuation tokens. If you re-run the wizard and provide the file again only the new updated documents will be processed.
Last but not least you need to set, if you want to update the provided continuation token file with the new continuation tokens which in most situations is desired.