Controlling a multi-zone AV receiver and cloud-based service like HEOS is among the more complex things that can be done with Hubitat, but it is possible.
@dman2306 can correct me if I’m wrong, but I don’t think the HEOS integration can set your receiver’s zone output (although it’s possible in the HEOS mobile app).
So to change your receiver’s zones you’ll need a driver that can do so. Unfortunately the Hubitat built-in Denon AVR driver doesn’t do this yet. There is a community driver developed by @thomas.c.howard that can do this though.
You could then create rules in rule machine that are triggered by the push of dashboard buttons. You’d need to make use of the custom action feature of rule machine and use either or both of the Denon AVR virtual device and HEOS virtual devices, depending on the dashboard button’s function.
So like I said, not the simplest thing Hubitat can do. But it can do it 
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Here’s the hub documentation pages, which covers a lot of topics, rule machine included.
If I could just ask, why not just use the HEOS app if you’re going to use a screen anyway? And same question re: Alexa voice control. The HEOS Alexa skill can be used directly to play music on HEOS devices.
