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Chronomancers have "countertemporal chronomines" as a Wargear option: in your shooting phase select an enemy unit within 18in and halve advance and charge rolls.

Psychomancers have the "Harbingers of Despair" ability, where in your morale phase, you can roll against the unit's moral and one of the options is to halve that unit's advance and charge rolls.

Both effects will at least affect that enemy unit the next time they do either charge or advance.

Which leads to: do these different named abilities stack? Example: Turns a 4in advance roll into a 1in advance and turns a 9in charge roll into a 3in charge (seems round up is the standard for other things that divide).

I see no reason why they wouldn't stack.

They look like they stack, so reduce a 12" move to a 3" move. Pretty frustrating for an opponent, methinks!

I agree.

Yes, they stack as they are not the same rule, just the same effect.

 Draco765 wrote:
Chronomancers have "countertemporal chronomines" as a Wargear option: in your shooting phase select an enemy unit within 18in and halve advance and charge rolls.

Psychomancers have the "Harbingers of Despair" ability, where in your morale phase, you can roll against the unit's moral and one of the options is to halve that unit's advance and charge rolls.

Both effects will at least affect that enemy unit the next time they do either charge or advance.

Which leads to: do these different named abilities stack? Example: Turns a 4in advance roll into a 1in advance and turns a 9in charge roll into a 3in charge (seems round up is the standard for other things that divide).

Unless rule in question says otherwise only same named aura's don't stack. Same named non-aura ability even stacks