Upgrade from OEM 11g to 12c: Clustered agents reported as "agents with Invalid Inventory"

We are in the process of upgrading our OEM 11g installation to 12c.
In the "Upgrade Console", agents installed to monitor a RAC were reported as "agents with Invalid Inventory".
These agents were installed using this method, in a custom Oracle inventory.
Additionally, from the "Setup", "Agents" tab, you can see a particular agent's page. There, by pressing the "Oracle Home" link, I was getting the following error:

Could not find Oracle Home <ORACLE_HOME> in the inventory collected for <HOSTNAME> on <TIMESTAMP>

As described in Oracle note 735952.1 - "Error Could not find Oracle Home in the inventory collected for on ", although some changes were necessary, to fix this problem:

• Edit $AGENT_HOME/sysman/config/OUIinventories.add
• Put an entry for your custom oraInst.loc, for example: inventory: /var/opt/oragrid/oraInst.loc
• Restart the agent
• From the OEM, go to the particular host's page, "Configuration" tab and press the "Refresh Host Configuration" button.
• Wait for it to complete and then go to your "Upgrade Console" and press the "Refresh Agents and Targets List" button.

Now, those agents are removed from the "agents with Invalid Inventory" list.