SQL Server CDC (Change Data Capture) Existing Data Seed
In case others end up here, a solution that works for me was to 


store data in a temp table
delete source table data
delete cdc table data
insert temp table back into source table


I had to build up a list of column names in order to insert the IDENTITY which accounts for most of the script. Below is similar to what I used, however I was running inside a loop of all of my tables. 

-- 1. Store data
SELECT * INTO #refreshTable FROM dbo.myTable;

-- 2. delete source table data
DELETE FROM dbo.myTable;

-- 3. delete cdc table data
DELETE FROM cdc.dbo_myTable_CT;

-- Build list of columns for insert
DECLARE @MyCursor CURSOR;
DECLARE @MyField nvarchar(max);
DECLARE @columns nvarchar(max) = '';
BEGIN
    SET @MyCursor = CURSOR FOR
        select [name] from tempdb.sys.columns where object_id = object_id('tempdb..#refreshTable');

    OPEN @MyCursor 
    FETCH NEXT FROM @MyCursor 
    INTO @MyField

    WHILE @@FETCH_STATUS = 0
    BEGIN
        SET @columns = CONCAT(@columns, ', ', @MyField)
        FETCH NEXT FROM @MyCursor 
        INTO @MyField
    END; 

    CLOSE @MyCursor ;
    DEALLOCATE @MyCursor;
END;
SET @columns = SUBSTRING(@columns, 2, 10000); -- Not expecting long column names

-- 4. Insert data back into source table
SET IDENTITY_INSERT dbo.myTable ON;
DECLARE @sql nvarchar(MAX) = 'INSERT INTO dbo.myTable (' + @columns + ') SELECT * FROM #refreshTable';
EXEC (@sql);
SET IDENTITY_INSERT dbo.myTable OFF;