Yup, as if the universe decided to prank on me (like when is it not), the answer basically fell into my lap just minutes after posting this.

In program one:

$out = `perl program2.pl "$var1" "$var2"`;
[download]

And in program two:

$output = "blah";
print $output;
[download]

And of course, it all works just fine for me.

*returns to banging head on desk