Just thought I'd post an update for anyone with the same issue. Given the System Report I figured I'd check with my client's host about updating the version of PHP running on the server, since it seemed possible that was the root issue. The host was able to update to a newer version of PHP and that seems to have resolve the 500 error issue fully. So if you're encountering the same issue I'd suggest opening a support ticket with the host to try and upgrade.
See: https://docs.woothemes.com/document/how-to-update-your-php-version/ for a quick explainer.