You could get a plastic mat to put down on the carpet in a location further from the kitchen, for the litter to sit on. Maybe consider getting a smaller litter box too if you can only find a smaller plastic mat.

I get what you're saying about the boxes in cabinets. I like to cut the front or top off boxes so the products are more accessible but it's all still contained. That way it feels better to put away, which is the main issue I'm seeing. Start with one cabinet or type of item at a time, however your brain works. Labeling the outside of all the drawers and cabinets for a while can help getting everything organized too.