As it turns out, the permissions issue was caused by SELinux. Thanks for the article.
Even after solving the permissions issue, though, I’m unable to share the folder. The VM will now start correctly, but Windows doesn’t recognize any of the drivers provided with the Fedora VirtIO Windows Guest package. I’ve got the iso mounted on the guest, but in Device Manager when I select “Browse my computer for drivers” on the unknown PCI device it takes about half a second to determine that none of those drivers will work.
While troubleshooting I also tried creating a Samba server on my computer to use from the VM, but I’m unable to connect to it from within the VM.