I liked your approach. I'm not sure you need the sub in it
though; you're already doing variable interpolation when you
open( OUT, ">$outfile" ) or die ... so you could lean it up a bit:
open( OUT, ">${_}_distilled" ) or die ...

Here's what your code inspired me to do

#!/usr/bin/perl

for(glob '*')
{
  /^$0$/ and next;  # don't process the script
  open(I,"<$_") or die("$_: $!");
  open(O,">$_.$$") or die("$_: $!");

  print O $_,"\n";
  { $. > 4 ? last : print O while(<I>); }

  close(I);
}

exit;
[download]

While writing and subsequently edting above program I discov-
ered the redundancy of local() in certain contexts. I originally wrote
{ local $_ = undef; $. > 4 ? last : print O while(<I>) }
RRedundancy bad, so local went away.

Update: changed >$outfile_distilled
to ${_}_distilled which actually makes sense
in the context of the original program.

blyman