Resolved.
Got help from a fellow member in the WP Membership site group: https://www.facebook.com/groups/membersitemastermind/66626490683538
At the top of checkout.php, is there a line of code like this:
<form id="pmpro_form" class="pmpro_form" action="<?php if(!empty($_REQUEST['review'])) echo pmpro_url("checkout", "?level=" . $pmpro_level->id); ?>" method="post"> If so, try replacing with: <form id="pmpro_form" class="pmpro_form" action="<?php if(!empty($_REQUEST['review'])) echo pmpro_url("checkout", "?level=" . $pmpro_level->id); ?>" method="post" target="_blank">