Another user found that aspnet_regiis is trying to add the user DOMAIN\user to the local group SERVERNAME\IIS_IUSRS.
He tried creating the group DOMAIN\IIS_IUSRS and that changed the error message from "The group could not be found" to "The specified local group does not exist"
The problem he had is the machine is a domain controller, so it's not possible to create local groups. With aspnet_regiis trying to add users to a local group, our install program is always going to fail.
He also discovered a group called DOMAIN\IIS_IUSRS~0 which appears to have been created at some point in the past, probably automatically. It was this group that had permission to access "C:\Windows\Microsoft.NET\Framework64\v2.0.50727\Temporary ASP.NET Files"
So he manually added DOMAIN\user to DOMAIN\IIS_IUSRS~0 and ran setup with the /ignoreisserorr and /ignorepermissionserror flags
He had to map the directory in IIS afterward, but other than that, so far it appears to be working.