Not sure this was intended, but I was able to beat the game by selling single cats after the debt pop up would appear.
It's better to keep your cats if possible and keep building up their value with the food clicks. If you wait for a cat to wander below the pop up you can still sell them instead of hitting sell all and losing all your growth. There is not enough time during the main game to select the cats you want to sell. So now any who wander into range can be sold . Then as soon as you hit your minimum needed you leave the rest alone and keep going.
This worked really well and I was able to complete it in a single sitting. However it would be much better to have a "cats" panel that sorts them by value and when the debt pop up launches people can still pick cats to sell at that time.
Definitely a fun game!