That all looks great to me -- good going! Recovery Tools looks fine in Disk Management.
(1) Your 2nd /Info is telltale...
C:\WINDOWS\system32>ReagentC /Info
Windows Recovery Environment (Windows RE) and system reset configuration
Information:
Windows RE status: Enabled
Windows RE location: \?\GLOBALROOT\device\harddisk0*partition5*\Recovery\WindowsRE
Boot Configuration Data (BCD) identifier: 06a7379d-d1bb-11ea-8997-b888e3b1b2f5
Recovery image location: \?\GLOBALROOT\device\harddisk0*partition6*\RecoveryImage
Recovery image index: 2
Custom image location:
Custom image index: 0
REAGENTC.EXE: Operation Successful.
(a) It says Partition 5 is now the "Windows RE location". That is, it holds the WinRE.wim that will become the recovery environment (Choose an Option) when you Shift+Restart (or whatever). And we know that is a 2004
environment. Go there, & "Troubleshoot > Advanced Options > Command Prompt" will show the same 2004 version you saw before: 10.0.19041.0.
Now, when the computer undergoes its next upgrade/repair install, the new WinRE.wim will overwrite (replace) this one in Partition 5. Also, Windows system image backup & restore will automatically select Partition 5 to backup as a mandatory, & Partition
6 will only be an optional (provided you put a letter on it). It used to look like this...

Now you'll see Recovery Tools instead of Push Button Reset as the mandatory one.
(b) Yet Partition 6 remains the recovery image location. If ever the button is found & pushed (or you try a Reset, I guess), the Install.wim that is in there will be restored. It will be Win 8 with a ton of Gateway
add-ons. That's what you wanted -- but I still think, really, Partition 6 should be dispensed with, & you should use your own system images instead which have all the changes you've made since 2012. There just can't be any good reason to ever return to Win
8 once you've got a working Win 10. In the worst possible situation (i.e., no image will restore), you would clean install Win 10. Any Gateway app that wipes out is likely recoverable at the Gateway site.
In any event, you need never make another image of Partition 6. It never will change from its 2012 date now that Partition 5 gets the new WinRE.wim files again. I don't know what happened in 2017 that made Windows switch
to Partition 6.
(2) Both XCOPY commands did what they should going by the DIR commands you showed. The second one overwrote a few files that had not been deleted by ReagentC /Disable, but mainly it replaced the WinRE.wim that had been removed. That's what you wanted.
(3) "But note, in This Computer, see image below, it now lists part 5, the Recovery Tools part. None of those partitions have ever been listed before."
Here is your Disk Management from page 7...

Partition 5 was listed, all right, but it showed differently because it had no letter or label. In that case, it shows the disk & partition number instead: Disk 0 partition 5.
(4) "AND it still has R assigned to the partition"
Well, I thought I was going batty when that happened to me. But my letter eventually did go. Try again & reboot. Or maybe it takes a reboot to the recovery environment (Choose an Option). Then, remove it at "Troubleshoot
> Advanced Options > Command Prompt"...
DiskPart <<< Enter DiskPart
List Vol <<< Shows the letters
Select Vol x <<< "x" is the volume that has the letter R
Remove Letter=R <<< Remove the letter R
List Vol <<< Show it's gone
Exit <<< Exit DiskPart
Exit <<< Exit the Command Prompt (or use its "X")
Click "Continue" to get back to Windows.
The letter has no ill effect except it makes the partition show up in File Explorer. Still, File Explorer won't show its contents, unless you play with Folder Options (type into Search)...

You have to uncheck "Hide protected...". But even then there will be a major battle with permissions before you can open a folder or file. But supposedly this makes the partition susceptible to hacking. So we do want the letter removed.
(5) "Re Acronis, does see Part 5 as the R partition. But in Full disk backup, it makes no difference, that shows all the partitions."
Yep, but you should backup Partition 6 just once ever, if even that many times. It never will change now.
(6) "The R does make a difference for file backup. In that, none of the partitions we have been working on show, except part 5 - because it is labeled as the R partition"
Partition 5 mainly is treated differently by Windows & 3rd-party apps because it is the active Recovery partition now. Where you saw extra attention paid to Partition 6, that attention now goes to 5 now. The letter & label do make a difference too, as you
saw in Disk Management & File Explorer.
(7) "Even in the theory that we could assign a letter to part 6 and then back that up, I do not think this is very easy, I'm sure things will get lost. This is not set up for very easy individual file backup."
I had a tough time detaching from my own Dell Win 8.1 factory reinstall partition too. I held onto it well into the various Win 10 versions. But mine wasn't intruding into Win 10 system images like yours was. There's no reason you should have more than one
image of it, if even that many. Your own Win 10 system images have everything you need.
But -- if you must have it -- show what I requested yesterday: "DIR X:\ /a /s" & "BCDEdit /Enum All".
(8) "But that allowed me to see files on part 5."
That sounds normal to me. Here is mine today...
C:\WINDOWS\system32>DIR R:\ /a /s
Volume in drive R is WinRE 2004
Volume Serial Number is 9AB3-01BA
Directory of R:\
07/27/2020 01:03 AM <DIR> $RECYCLE.BIN
07/27/2020 12:35 AM <DIR> Recovery
07/28/2020 03:28 AM <DIR> System Volume Information
0 File(s) 0 bytes
Directory of R:$RECYCLE.BIN
07/27/2020 01:03 AM <DIR> .
07/27/2020 01:03 AM <DIR> ..
07/27/2020 01:03 AM <DIR> S-1-5-21-191566122-1535656984-3147892972-1001
0 File(s) 0 bytes
Directory of R:$RECYCLE.BIN\S-1-5-21-191566122-1535656984-3147892972-1001
07/27/2020 01:03 AM <DIR> .
07/27/2020 01:03 AM <DIR> ..
07/27/2020 01:03 AM 129 desktop.ini
1 File(s) 129 bytes
Directory of R:\Recovery
07/27/2020 12:35 AM <DIR> .
07/27/2020 12:35 AM <DIR> ..
07/27/2020 09:34 PM <DIR> Logs
07/28/2020 01:30 AM <DIR> WindowsRE
0 File(s) 0 bytes
Directory of R:\Recovery\Logs
07/27/2020 09:34 PM <DIR> .
07/27/2020 09:34 PM <DIR> ..
07/28/2020 01:30 AM 1,384 Reload.xml
1 File(s) 1,384 bytes
Directory of R:\Recovery\WindowsRE
07/28/2020 01:30 AM <DIR> .
07/28/2020 01:30 AM <DIR> ..
12/07/2019 05:08 AM 3,170,304 boot.sdi
07/28/2020 01:30 AM 1,139 ReAgent.xml
07/09/2020 11:23 PM 525,321,603 Winre.wim
3 File(s) 528,493,046 bytes
Total Files Listed:
5 File(s) 528,494,559 bytes
16 Dir(s) 341,311,488 bytes free
It's got its Recycle Bin back with just a Desktop.ini inside a GUID folder. And it looks even worse in the recovery environment (Choose an Option)'s Command Prompt showing the other stuff you mentioned. It's normal let's presume. The main thing is that Shift+Restart
(or whatever) gets there & it works. And I thoroughly tested it.