If you're setting the &propertyMode= parameter to value_and_history, then you should be getting the full property history for each property. This might only be a single value if the property in questions hasn't been updated before. Without a concrete example, I'm not really able to dig much deeper into this. Feel free to DM me any details you don't want to share publicly.
Are you replacing the demo hapikey with your own hapikey? Can you give me an example contact that has history you're not able to see with that request?
You should be getting all contact properties that have a value, and by including propertyMode=value_and_history you should be seeing the history for each of those contacts. Are you including a &property= parameter as well? Can you give me a link to the contact in your portal you're trying to get the history for?