For what it's worth, I was able to work around the problem somewhat by using Terminal.app to start the tech preview with the sudo command. This allowed the virtual machine to start, though I had to re-grant all of the required permissions. Starting TP normally via the icon in the Applications folder still yields the error though, and I suspect starting with sudo is not the most secure approach.

To get the permissions to work I had to enable the root account by way of the Director Utility, log into it and start the tech preview there so as to allow the program to prompt me for the required permissions, then I logged out and back into my normal (administrator) account.