You've already acknowledged that it wasn't smart to ignore the warning, so I won't belabour that point (though I certainly agree with your assessment).
The easiest thing to do would be to create a new partition at the proper location and restore your files from a backup. However, I'm assuming that "I don't want to format it" means "I don't have a backup".
In that case, it will likely take hours of work to repair, even if you happen to know the exact offset where the process stopped. The beginning of an NTFS filesystem tends to contain some of the most important information, including the Master File Table (MFT). There is a second copy of the MFT on the disk, but there is a high likelihood that any files that had fragments in the moved section of the disk will be irretrievable, if you can mount the filesystem at all.
If you choose to go ahead and attempt a recovery, you should take an image of the drive before running any tool that writes to the drive. This includes
chkdsk with the
/f flag. This will ensure that you can always revert to the "least-broken" version of your drive.
chkdsk is able to repair your drive to a state where it can be mounted, it is unlikely that it will be bootable (if it is a boot drive). In this case, you may be able to boot another operating system, mount the drive, and recover some of your files.
If you're able to ascertain where the move process left off, you may be able to reverse the process: however, this will almost certainly involve writing custom code to shift the data back.
Good luck. Please remember to back up your important data to avoid problems like this in the future.