Quick update (no gifs, sorry):
I've tweaked the hitboxes so that any part of a cat hitting the basket counts as a hit, but the dogs can only be "caught" if their bottoms hit the top of the basket.
I've also slowed the basket down slightly, but implemented a "turbo" button to allow you to move faster. Basket speed was "3" before, now it's 2, with turbo being 4. Should make weaving through the cats more doable.
Going to make the cat collisions do something next, aside from decrement the lives counter. I'm thinking explosions with fireworks.