I think I figured out a way to do this. It's clunky, but it works for me. It's necessary to have at least one installation that will boot. It's also necessary to have Windows installation disks for the OS's you are cloning. You don't have to have activation codes for them, just the ability to install with or without activation.
First, create a partition a little larger than the size of the installation you unsuccessfully tried to clone.
Second, using your installation disk, install Windows on the partition (or disk) that you had just created. After that installation, you can boot into it.
Now you have two bootable partitions, the original good installation and the new "throwaway" version.
Third, reboot into the original "good" installation and use Easy BCD to add that the throwaway installation. On reboot, you should have the ability to boot into either the original or the throwaway version.
Fourth, re-clone the OS of the formerly unbootable installation to the same location where you just created the throwaway version. The cloning software (or command prompt) will overwrite the throwaway version.
You should now be able to boot into either the original version or the cloned version. You can do this with any number of partitions.
Here's the takeaway: Each time you install Windows, you create a bootable partition (or disk). The partition is bootable because you directed Easy BCD to add that partition, even if you delete its contents and copy or clone another installation on to it.