CDC capture job failed. Now I need to recover missing inserts

We utilize cdc for auditing purposes for changes to our user attributes, and their authorization to our role based solution. During a recent deployment we realized post deployment that change data was not being written and discovered that the change data capture job had failed several hours earlier. We have determined how to get the capture job up and running again.
CDC is enabled, but cdc.dbo<table-name>_CT table is not being populated

Now we need to recover inserts and updates that happened while the capture job was down. I can get that data, but I have no clue how to go about inserting the data into our cdc capture instances. Is such a thing possible? I know the $operation value. Can I get the $start_lsn from the Transaction Log? What about $seqval, and $update_mask? We inherited the cdc implementation, and have sparing knowledge of how it works, especially when it doesn't work.

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