My solution in the past has been either to write 2 functions or else to pull the following trick:

sub foo {
  my %args = (1 == @_) ? (named_arg => shift) : @_;
  # etc
}
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or pull it as follows:

sub foo {
  my $args = shift;
  if (! ref($args)) { # <- test depends on usage
    $args = {named_arg => $args);
  }
  # etc
}
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Now it can be called two ways. Internally that is turned into a hash of named arguments, and then I can proceed to supply defaults for whatever is missing.