I like your ideas and agree that there is problems with gpu cases.  Would be great if you can make something compact and quiet, and secure.

I think for this vertical design to work well specific gpu brand cooling would be needed.  MSI has horizontal fins that mimicks active cooling heat sinks.  Evga heatsinks are vertical fins so air does not flow as well.

A question about the rounded top of your case? Is this so you can stack multiple cases on top of each other? If so sounds like a good idea so heat isn't transfered to the stacked case

Seems like a simple box top chassis shape would be cheaper and good for airflow however cases can't be stacked.

Awesome keep up the good work and can't wait to see this get tested. 

Where will the power supply be located? What type of power supply can it support? I'm assuming something like an evga 1600 watt would be supported?