The issue with $" has already been answered, but I just wanted to put out something about the regex you're splitting on:
my @record = split /(["<",">"])/;
You've got a character class there, with some redundant characters. It's actually equivalent to the character class
["<>,]. I'm not sure if that's what you meant with the quotes and the comma.
You're also getting the delimiters in your resulting array, because of the capturing parens in the regex.
Here's another way of solving the problem, that I think is a tiny bit simpler:
while (<OLDFILE>) {
chomp;
my($last, $first, $email) = split /, */;
$email =~ tr/<>//d;
print NEWFILE "$last, $first, $email\n";
}