If your setup is just like you showed, you can do it with a formula
pretty fast.

In C1:
=IF(A1="","",IF(B1="",A1,INDIRECT("C"&ROW()-1)))

Copy down all the way to the end. Then copy C column and Paste Values.
You can get rid of the extra lines fastest by doing a Sort on the B
column. It should group all the old "header" rows and you can delete
them quickly.