So very often, these types of questions remain fully mired in the realm of naked mechanics, but I find it helpful to imagine what's actually happening in the fiction. The mechanics are there to aid the fiction at the table, after all.
So, what's taking place during Stay Down!? How is the creature keeping the target down?
To me, this has real "stomp" energy, where the user is putting their foot on the target's back, or dropping a knee on them, or something, while yelling at them to stay down. The target tries to get up, but is forced back down to the ground before they can really move -- after all, if the prone creature can get up into a plank position, or up onto their hands and knees, it becomes significantly harder to force them back into a prone position.
That is to say, it happens very early.
Reactive Strike, on the other hand, is about looking for openings to strike, where the target has let their guard slip (or abandoned it altogether). This is why it applies when the target is trying to stand -- it's very hard to defend yourself from a determined attacker when you're transitioning from lying prone to getting into almost any other position.
But when the first creature uses Stay Down, they are functionally putting themselves between the target and anyone else who might want to strike. An ally might not want to take the chance in this situation, particularly since the fiction is not "attacking someone who's being held down", but "attacking at the same time that your ally is getting in the way".
Topple Foe, on the other hand, is entirely about taking advantage of a distracted or staggered target and trying to sweep or tackle them to the ground. And unlike Stay Down! and Reactive Strike in the first example, it doesn't even have the same mechanical trigger as the reaction you're trying to pair it with. This is just a pure tag team shine spot.