When every sector has been overwritten, the data is gone for ever. A formatted drive or one where files have been deleted can be recovered but one where every sector has been written to, the previous data is gone forever.
Contact your company you listed and tell them that you accidentally wrote new data to every single sector on your hard drive. Ask them if they can retrieve your old files. They can not.
Old "signals" (writes) remain on the magnetic media. This has nothing to do with logical organizations of binary data such as sectors. It's at a lower level. It's all about residual magnetic flux.
Many of the comments at the bottom of the post are informative. I believe the last comment to be correct: given a strong enough reason, forensics can be effective.
The company I mentioned has many levels of recovery services, including the very low level analog stuff.
I hope this helps explain where I was coming from. ;-)