Well, for anyone else looking to solve a similar problem, I found this post, and it led me in the right direction: http://wordpress.org/support/topic/pagination-on-singlephp-causing-301-redirect?replies=9.
I added this snippet of code to my functions.php, and I can paginate in custom queries without issue on single.php now. I don’t know enough about it to know what it does, but it seems to fix the problem!
add_filter('redirect_canonical','pif_disable_redirect_canonical');
function pif_disable_redirect_canonical($redirect_url) {
if (is_singular('pov_channel')) $redirect_url = false;
return $redirect_url;
}