I never received a response to this issue, and never figured out why the reCaptcha wouldn’t load. Unfortunately, I had to abandon this plugin as a result. It’s a shame that this minor issue ended up sinking what was otherwise a perfect solution to my client’s needs—without a reCaptcha in place, his inbox got flooded with spam.
Sorry I can’t be of more assistance, @khermberg. I hope the plugin author fixes this critical flaw eventually.