What could be preventing my Mac Mini 2011 from completing the boot process?

You're right, Recovery mode has to be working for you to get anywhere.

I am wondering if it is actually booting Recovery mode or not, since Recovery exists on a separate and normally unalterable volume on a High Sierra system. Its boot process does not load from the volume giving you trouble. Same uncertainty with the USB flash drive. It shouldn't be stalling at the same point.

First question: are you using a standard Apple keyboard? The reason for asking is that the usual ⌘ R key chord might not work if the ⌘ key is not properly mapped on a non-Apple keyboard.

Regardless of that answer, it appears booting the built-in Recovery volume is not working. In that case try forcing the Internet version of Recovery to load by adding an option key to that key chord. In other words hold ⌥ ⌘ R (three fingers) while you start your Mac Mini with another finger. That will result in an obvious change to the startup screen: you will see a "spinning globe" icon as it loads Recovery from the Internet. That doesn't load anything from the startup disk at all. You could disconnect it; completely remove it from the Mini, and it would still work.

Try that and let me know what happens.

By the way since you're trying to get the boot volume to load there is no harm in running fsck in Single User mode as many times as you wish, until you give up. In rare cases I have found concerted multiple repeated efforts succeeded, long enough to reformat the drive, and continue to use it for at least a little while.

I agree. After having done everything else, you effectively isolated the inability to boot to something other than the startup device itself. That leaves little more than the logic board or something connected to it. In particular, I would suspect the GPU is defective, the reason being the line shown in Verbose Mode:

IOConsoleUsers:gIOScreenLockState 3, hs 0, sm 0x0

That log entry has something to do with the GPU. If the Mac stalls, shows a grey screen, and reboots about half a minute later it suggests the attempt to initialize the GPU fails for some reason. From what I can determine it appears to have been commonly encountered when attempting to install macOS on non-Apple (i.e. "hackintosh") hardware, and that's pretty much where my curiosity ends.

As you determined Apple Hardware Test is of limited value in exhaustively diagnosing every potential factor. (Apple Diagnostics doesn't apply to that model).

So where do you go from here. Knowing that era was marked by AMD GPUs that were prone to an early demise might be additional justification for suspecting it as the culprit. Since it is not a socketed module like it is on some Macs, if you are sufficiently motivated to fix your Mini I suggest the next step is to obtain a replacement logic board from a reputable source.

Needless to say I wouldn't spend a lot of money on it, but I think that's the next logical step.

The boot process is probably encountering a corrupted file which in turn loads a corrupted operating system process that crashes the Mac.

Not that it matters. That corruption should not have occurred to begin with, but the solution is to reinstall High Sierra. The easiest option is to restore a Time Machine backup created prior to the onset of corruption. Whatever caused that file to become corrupted is likely to occur again, but that might not be for years. Restoring the Time Machine backup will restore High Sierra on that Mac.

No Time Machine backup? Things get tedious. As I recall, that Mac did not ship with discs, which means you have become caught in the brief era in which Macs did not ship with discs, but for which OS X Recovery won't work any more. There is a workaround but it's tedious. Read How do i fix "the recovery server could not be contacted" … - Apple Community for one recent example. Be advised I have not tried it so if you need help with that procedure I'm not the one to ask.

You wrote that you booted from the Install Mac OS USB flash drive. Does the same thing happen, and does it appear to happen at the same point in the boot process? I am wondering if the Mac is in fact booting from that device, or if it fails over to the usual startup disk with all its problems.

Apple Hardware Test / Apple Diagnostics does little more than test for the presence of operable hardware. As such it cannot be used for determining operating system file integrity.

Examine your video and determine if you can read and describe the last readable message before the Mac crashes.

Sounds like the hard drive is most likely failing if you cannot boot into Safe Mode. A failing hard drive can also prevent successful booting of external media such as USB sticks and even Internet Recovery Mode (Command + Option + R).

FYI, Single User Mode can be accessed by holding Command + S immediately after the startup chime.

Disconnect the SSD and see if you can successfully boot into Internet Recovery Mode or to a bootable macOS USB installer. Unfortunately not all SSDs are compatible with all computers. If the Mini is still unable to successfully boot to the installer, then you have some other sort of hardware issue.

Try running the Apple Diagnostics to see if any hardware issues are detected. Unfortunately the diagnostics don't detect most issues.

I think you reached a conclusion.

The reason AHT / AD is of limited value is that it can only positively identify a definitive fault. In other words if it concluded with a VFD001 code it might mean Diagnostics merely attempted to communicate with the GPU and it didn't respond. A similar code in AHT might be 4YDT but that's little more than a guess on my part because Apple doesn't publish the meanings of those codes.

I surmise the particular fault in this case is an inability to correctly process an initialization command, probably because the display driver hardware invoked by those commands isn't working despite the GPU being able to communicate them. That's also little more than a guess, but it's as far as we can take it.

The only reason I suggest using those diagnostic tools is to confirm a problem that you probably already suspect. It can't always do that though, and it might just conclude "no trouble found" when trouble obviously exists.

Since you're interested in keeping the Mini as a spare, a replacement logic board might be worth the effort, if you can find one inexpensive enough. They're all going to have the same life-limited GPUs though.

... choices between internal recovery, Macintosh HD, USB install and Time Machine backup, ...

But if you get to that point (the four choices) I recommend reformatting the startup disk. Isn't Disk Utility one of those choices?

That's Recovery mode. It wasn't clear to me whether you got to that point or not. Actually it's still not clear to me, but that's the goal for now.

Use macOS Recovery on an Intel-based Mac - Apple Support

John Galt wrote:

As you determined Apple Hardware Test is of limited value in exhaustively diagnosing every potential factor. (Apple Diagnostics doesn't apply to that model).

FYI, while this model shipped with the AHT on the internal drive, this model did acquire the later online Apple Diagnostics after macOS 10.12.4+ (IIRC, certainly if 10.13) was installed which modifies the system firmware to allow access to Internet Recovery Mode and the online Apple Diagnostics. AFAIK, all Macs capable of running macOS 10.13 High Sierra from about Late-2009 to 2015 acquired both Internet Recovery Mode and the online Apple Diagnostics after having installed the macOS 10.12.4+ update.

AFAIK, all Macs capable of running macOS 10.13 High Sierra from about Late-2009 to 2015 acquired both Internet Recovery Mode and the online Apple Diagnostics after having installed the macOS 10.12.4+ update.

Not all Macs acquired it. The earliest Mac I have that did was a 2014 model, but none of my earlier models running HS incorporated AD nor did it ever become available for them.