I didn't write that very well, I meant the screen going blank (guess I shouldn't call it a screensaver). I just tried it again, setting 2 minutes using Siri, screen went dark quickly, and the alarm worked. Tried it again, setting 2 minutes via the Clock app (accessed from the Lock screen), and the screen darkened at about 1:45 but was still visible, and right at 2:00 the timer hit 0:00, the Lock screen turned on again, no alert, and then went dark.
So, apparently 26 gets confused when the screen is just about to go blank, I guess. Weird.