> Up to once a week, now, iCloud (in OS X settings) asks me to verify my password when "nothing has changed" (no purchases, etc). It then spins for a long time and there's no acknowledgement that it 'succeeded'.

Only once a week?

Try refusing to log in. You'll get pestered every five minutes, sometimes more often than that.

Try disabling it after not logging in, and it asks you to log in to disable it, and then start pestering you even more frequently. Completely asinine.