Cannot delete / remove +-1TB of Temp Files on 1/2TB Drive?

You could try WizTree to see if it can show where the 52 GB of Temporary files are.
You can click on the [+] icon next to a folder name to expand that folder and see what's in it.
If these temporary files are small files scattered all over this might not help, but it's free to try.
They have a Portable Zip available, no install needed.
Antibody Software - WizTree finds the files and folders using the most disk space on your hard drive

You could also try WinDirStat.
Make sure you have Shown Unknown checked in the Menu/Options
WinDirStat - Windows Directory Statistics

I just tried antibody and here is what it showed me:
While NEAT attempted to uninstall all of their Software, it appears it did not work 100%
Antibody shows a number of NEAT "pieces" left behind.
I am unsure what the letters HSC on the right side of the List mean.
Perhaps the GB's that cannot be deleted by the MS Disk Cleaner are these NEAT residue items.
I sent the list Antibody produced to NEAT via email as they are not open on the weekends.
I'll report as to their summation / action when they respond next week.
Thank you for the referral to Antibody as it's a new place to look and potentially a solution / fix.

Your screen print is for a Recycle Bin.
Have you Emptied the Recycle Bin ?

The Recycle Bin on my Desktop, has been emptied many time during this process, regardless if it has content or not.

Why they appear to be in a Recycle Bin is beyond me, but I am a Novice at this.

What does the $ imply in front of some Files and not others?

YIKES, A ghost Recycle Bin!

Late to this party, but since you're still hard at it Mike Lynch what I would do is boot the PC with Puppy Linux, and use it to remove those Recycle Bin items at least.

Puppy might also show you junk that Windows is hiding from you. But use with caution of course. BTW if you use System Restore, have you tried turning it off (assuming you have no need/interest at this point to go back in time)? Turning it off should delete all Restore Points which are also hidden in Windows.

After doing any of this you should run chkdsk yet again I think.

A corrupted Recycle Bin can be fixed in Windows, here's a tutorial:
Recycle Bin Corrupted - Cannot Delete File or Folder

That probably wouldn't explain/fix the 52 GB of mystery temp files.

As suggested by maxseven Puppy Linux might help find the files.
As suggested by Callender BleachBit might help find the files.

Did you run WinDirStat and see what it shows for Unknown ?
Some Windows programs can't read all files and might show as Unknown space used in WinDirStat.

Well, it's not a happy ending! After multiple attempts to reach NEAT I was able to have them attempt to clean up my System again. Their attempts failed and as a result of those efforts, my Desktop was flooded with about 40+ old Files, Folders and Short Cuts. On seeing there efforts failed, I was contacted by another level of support in the Pacific. I spoke with them and then they contacted the Support Person who last worked on my System. The rep from the Pacific called me back and referred me to Microsoft. I believe I will just have to live with this a the time invested by the Forum, NEAT and myself is just way beyond belief. I intend on trying to use Easy File Transfer to "migrate" from my current W-7 System Disk to a freshly installed W-7 System Disk. I will report back if it resolves the issue but my purpose in the Transfer is to eliminate unused Software, eliminate duplicate Files and improve the speed of my System. Thanks for trying to help me, I appreciate you efforts.

I neglected to ask: is there a Telephone Number or Email Address that I could use to report a situation like this to Microsoft? I do not believe they would want to help since the problem was caused by non Microsoft Software but I'd call or email them if I could get to the most logical Department easily. I guess I am frustrated and I do not relish phone trees, explaining the situation multiple times and "I think you understand". I wish I never gave the NEAT Desktop Scanner a second try. The first time should have been a lesson to me. The day after I bought the NEAT Scanned, at a discounted price, Sam's Club cleaned the shelves and their WEB Site of the Desktop Model. Something wasn't right for them to do that. If the Forum could "refer" me to a Microsoft Phone Number or an Email Address for this type of situation, I'd appreciate it.