Magento2 Layout XML – Where Layout Handles Are Defined by a Module

Since you are using your own controller you don't need to only use the default handles. Based on the logged in status you could add in your infoAction method

 $this->getLayout()->getUpdate()->addHandle('mymodule_customer_info_logged_in');

or

 $this->getLayout()->getUpdate()->addHandle('mymodule_customer_info_logged_out');

and then in your layout.xml file use

<mymodule_customer_info_logged_in>

and

<mymodule_customer_info_logged_out>

-- addition after your edit below --

Seeing that you don't want to edit the controller (since it is a 3rd party extension), I would create a separate extension that only observes controller_action_layout_load_before

    $update = $observer->getEvent()->getLayout()->getUpdate();
    $handles = $update->getHandles();

    if (in_array('custommodule_customer_info', $handles)) {

        //code to add the custom handles based on login
    }

<update handle="foo_cat_a" /> might not work because it is likely being parsed before the handle (which typically adds the product.info block handle) is being parsed.

To debug handle load/merge order you can follow the directions I have specified here