I managed to solve this by removing the WooCommerce Layered Nav widget from my widgets for those dealing with the same issue… and it’s probably because I’m not using the Woocommerce attributes for my product: https://docs.woothemes.com/document/woocommerce-widgets/
I just discovered this on my only site managed with MT. Other hosts do not have the same issue as far as I know. With that said, the fix that MediaTemple put up at https://wiki.mediatemple.net/w/WordPress_Redirect_Exploit did solve this issue and I’m in the process of changing database password – oh the joy.