Hi Jeff
You should not do recording all the empty column( New Entries). You do like this select copy as icon for 1st record it will display one entry you enter necessary data and save. Then automatically in LSMW it will loop as per the no of records one by one it will process. This way you issue will get resolved.
By this way recording it will capture only one record and but you can process all records successfully.
Thanks and Regards
Vijay