This is truly a perplexing problem. Here's a possible solution involving pipes: (tested code)
in reply to Closing and re-opening the DATA Filehandle
It kind of shocked me that *DATA was not read-only. After reading from the pipe, just write the same thing back and you'll have an infinite supply of DATA. This can be easily adapted for lines of DATA but be beware of autoflushing. I came across some pitfalls involving non-flushing data in the handles when I was doing something similar.
pipe(READ,WRITE) or die;
READ->autoflush(1); #just to be safe
print WRITE $data;
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