SFTP Chroot and SSH

I have a chrooted SFTP user group to access my home server. The chroot location is /mnt/, mostly because it is already owned by root and is where I have mounted the external HDD I want to the chrooted user group to access. Moreover, I got 'Permission Denied' errors when I had the chroot directory at /home/[user] (even after assuring that it was owned by root)

I've generated RSA keys in order to disable passwords authentication entirely, but I can't copy them to the home server because my chrooted user does not have write permissions to /mnt!

Is there any workaround?