Observed Behavior
If Custom Fields don't appear in the drop-down of certain Activities in Experience Designer, check the configuration of the custom field. It may be a field created under the "CO" package of Service Cloud. These fields must be referenced differently than other custom fields within Service Cloud.
Sample resolution
Let's say you want to reference: \\ CO \ Incidents \ Custom Field Name
You would manually type the following reference in the Activity:
CO$CustomFieldName