OK, I switched to an Apple-branded USB-A to Lightning cable and Klein ET920 tester, verified with an Apple 10W USB charger that it did 5.07V 1.68A on an old iPad Pro with Lightning connector (it was 87% full so probably not drawing at its fullest).

When put on the Nitecore on, it did the same 5.07V 1.56–1.68A whether I turned on slow-charge mode or not. At this point I think it's a placebo, and if you want fast charging up to the rated 18W you must use USB-C, but on USB-A YMMV depending on the cable.

This also confirms my feeling that every power bank maker should adopt the Anker 737's status display feature, and that a USB multimeter is a must-have accessory.