I'm not sure I am following you.
What about this procedure:
Get the new HD and install it.
Disconnect the current OS drive C
Boot from your Macrium recovery disk.
Navigate to your image of C file on your backup drive. Restore it to the new drive.
Reboot to the new HD which now has the restored image of C.
I would think that in that scenario, the new drive would automatically have the C drive letter.
I use Macrium, but have never restored an image with it. However, that is the procedure I would attempt if I had to restore.