Pet Shop

[locusts]

Additional idea. Have them spawn via a leash you apply to your arm. And let them be removed similar to bandage removal. Thus the pet is simply constantly pulled behind you (though I suppose that seems mean when I picture it in my head. )

Coincidentally I was going to suggest a leash as an item. Use it on a pet or critter and its movement becomes restricted to the free tiles next to you. Use it on the leashed pet again to set it loose. You can even tie leashed pets to handy posts, and they will be restricted to movement about that post.

For entertainment value, I'd suggest the only things that can't be leashed are Jones (because cats are obstinate like that) and humans (because this isn't that kind of game). Anything else is fair game. Take George for a walk around the ship! Drag a terrified Morty playing dead down the corridors! Tie some space wasps to a post to keep people away! Feeling brave? Try and take a wendigo for a walk!