One of the more recent streams, Salty did say that the devs are aware of the issue and are considering ways to address the problem. If I remember right, a potential solution was to allow the player to choose from a pool of possible rescues when one spawns was being considered (absolutely nothing concrete yet, though).
If there isn’t a QoL light update for the holidays, the next update after 4.6 should finally be the big PvP update as there are no more legacy systems that are left to convert after 4.6 launches. If the standard PvP gameflow is altered then, I expect the pet rescue solution (whatever it may be) to be implemented with that update.