reCAPTCHA does have an audio option, and it seems to be accessible to screen readers, as detailed in this blog post: http://terrillthompson.com/blog/682
When the checkbox is clicked, a visual puzzle appears; right below, there's a button that can be clicked to switch to the audio captcha. Here's a demo: https://www.google.com/recaptcha/api2/demo
Thanks! That should have been Cloudflare support's answer. I did not detect the three pictograms as they were contrast-"enhanced" away. The non-visual reCAPTCHAs I now get are even passable without sound.