This makes sense. Then it's sufficient to make a program abortable and it will also service preemptive computations.

In my question I said that I already tried AbortQ and that it did not work. I must have done something wrong, or perhaps didn't call it frequently enough. Now I tried again and it works.

I didn't know this myself until it came up in discussion recently. The right way to do this is to call libData->AbortQ().

Which makes sense given what I know of the kernel implementation. Both aborts and preemptive calls are kinds of interrupts, and I'm pretty sure that the implementation of interrupts in the kernel consistently checks for and services every kind of interrupt. But I agree that the name doesn't suggest this, and the documentation doesn't state it.