The theory is that restoration of the Exchange databases isn't supported by IDR, but the server itself is. Restore the server using IDR, then restore the Exchange information store, using the Exchange agent.
I haven't used IDR myself. I know that there used to be some disquiet about it, though that seems to have died down recently.
To do a disaster recovery of an Exchange server, you don't need to install Exchange in disaster recovery mode, provided you've backed the server up properly. Instead, restore the server the normal way (install Windows, install the remote agent, restore all drives, system state and shadow copy components, reboot). Then the server will start up, though Exchange has no information store data yet, so set the information store to be overwriteable, then restore it from backup using BE.
I've performed this procedure many times, and can confirm that it works!