Can you choose a different ability for Hex when changing its target?

As a corollary to “Does reactivating Hex have any spell Components?,” is the player allowed to choose a different ability when cursing a new creature as a bonus action? RAW, it reads as a no, but a RAI argument could support a yes.

The warlock isn’t recasting Hex after the initial contact dies; instead, he maintains concentration on the spell and shifts the focus of the spell to a new target via a bonus action on a subsequent turn. The spell doesn’t say it must be shifted on the subsequent turn following the death of the target. Rather, it may be moved on a subsequent turn. Relevant text of Hex follows:

Also, choose one ability when you cast the spell. […] If the target drops to 0 hit points before this spell ends, you can use a bonus action on a subsequent turn of yours to curse a new creature. (PHB p.251, emphasis mine)