I'm happy with the resulting script. It's far more clear and far less ugly. Regarding some of the bogosities in my postulate:

• Obviously, the line-by-line processing depends on whether the data file has each group of records on one line, or each record on a separate line. I went for the first assumption (as it makes more real-world sense to me) and you went for the second (as you had the patience to View Source).
• That also lets me get away from the push reference position bit. Not a big loss.
• I thought avoiding the implicit local $_ behavior in the while loop would be more clear for the OP.
• People don't use split and join nearly enough.

Well done.