Well, I finally found a solution to this randomly recurring nuisance.
In the seven months since I first posted this question, my Windows 10 workstation rearranged my MIDI interfaces five times. Five times! No USB cables were moved. No system changes. Nothing.
Asking Windows to put your device back isn't an option, but I discovered a way to cleanse Windows' memory of the device so that it can be reinstalled, as if for the first time. Consequently, if you have one MIDI interface, it will appear as device #1, and if you have three, they'll be #1, #2, and #3
(per your order of installation). Best of all, this is achieved in just one click. Here's how:
- Download and install the free Device Cleanup Tool and Device Cleanup Cmd from Uwe Sieber.
- Turn off your MIDI interfaces and use the Device Cleanup Tool to locate all relevant device entries. If you're unsure, turn on your MIDI interfaces, refresh the Device Cleanup Tool display, and note which "non-present devices" disappear. Repeat as necessary.
- Open the Properties dialog for each relevant "non-present device," choose the Details tab, and then locate the "Device instance path" property. Note the commonalities in each entry. You will need to produce pattern strings that match all of the relevant entries exclusively.
- Launch a command prompt with Admin privileges.
- Test your patterns by executing Devicecleanupcmd with the "-t" (test mode) option. Consult the documentation and refine your patterns until a single command locates all of the relevant "non-present devices" with no false positives.
- Record the command (without the "-t" option) in a TXT file and save it to your desktop as CLEAN_MIDI_DEVICES.BAT, for example.
- Embellish your batch file as desired. In my example, below, I've added prompts to verify that all MIDI interfaces are powered off. [Otherwise, the process won't be successful.] If you've got a lot of interfaces or are otherwise forgetful, you might also want to remind yourself in which exact order the devices should be re-powered up.
Now, any time Windows reorganizes your MIDI interface(s), simply shut them down, run the batch file
(as Administrator), and then restore power to your MIDI interface(s) in the appropriate order. Your driver software wasn't deleted, so Windows will automatically locate and install the necessary components, and things should be restored to a "Windows Clean Install" state.
Here are some supporting images:
First, the Device Cleanup Tool. In my case, all of the myriad "MIDI" and "MOTU" devices must go.

Here's one of the device instance paths I'll build a pattern for. In this case, discovering that VID stands for Vendor ID, a Google search reveals that 07FD is indeed MOTU's assigned vendor ID, making it an ideal search pattern for at least some of the devices.

Here, I'm testing a pattern. Per the docs, asterisks (*) are wildcards.
And here's my final batch file. Note the three patterns in the DeviceCleanupCmd line and that the "-t" option has been removed.
Please be careful. Though these tools are supposed to remove only
"disconnected" devices -
how much harm can that do? - I suppose it's still possible to remove something better left alone. And if you live in my world, anything that can happen.... Well, caveat emptor.
I hope this is helpful.