With Nana Morri's deals pulling from your deepest desires, it makes so much sense that Orym would ask for what he did. The core tragedy of his backstory is that he lost those he loved and wasn't able to protect them. Now, going into this high stakes fight, it's partly "make sure we're successful" as an end state but its mechanism: keep me from losing anyone. Make me powerful enough to protect them (this time). On the surface it's selfless - protect others, achieve the critical goal - but if they are all successful, Orym will then be leaving behind his home and the Ashari and otherwise stepping away from those he loves, which could hurt them.
Chetney's deal is interesting too, for all that it's more classically "selfish" on its surface: his story has been a long and varied one, with family leaving, associations and partnerships coming and going, a traumatic transformation of the self with his lycanthropy, guarding himself from getting attached to people, and underlying all of it a deep passion for his craft. His desire to be the most famous (notorious) toymaker is about recognition but also about consistency and stability. If he is the most famous toymaker, he will have made his mark (in wood), people knowing who he is, having a reputation, a self beyond the self. Aging and death are also specters of change, and the earlier version of Chetney's desire was about youth or immortality.
If Orym is asking not to lose anyone else, Chetney is asking not to lose himself.
