Why is my iOS Reminders app slow and unstable when invoked by Siri?
The fix to this problem is due to the fact that the reminders list that it was attempting to add to (... which is the one that was configured in iOS as the "Default reminders list") was a very old and very full list.   It was not super full of un-completed reminders, but the number of past COMPLETED reminders was over 8,000.

So, to fix the slowness, I simply created a new reminders list in my iPhone. Then I configured this new reminders list to be the "Default reminders list." 

After that point in time, Siri commands to create new reminders work smoothly and quickly.  (AND, related to that final bullet, this new reminders list was fully visible, not empty, in the iCloud web app.)