I don't yet have a test instance ready for you, but I do have more information. The saved search returns no records in Kanban field only if the criteria saved in advanced search is a relation. For example, if we had a module called Widgets that is related to Accounts, and wanted to view all Widgets having Account = "Vedisoft". It seems not to matter if it is a custom or a standard module, nor if the relation was created in Studio or Module builder.
Our initial application for the Kanban view has 9 columns, and I believe everyone here uses 1080p displays. It would not be problematic for the text to be the same size as now and for it to simply wrap to the next line. The zoom feature in a browser works but the text becomes too small to be useful.