Wow! It's like reading about a parallel universe. My daughter is 6 and life is much like this around our house, which is smallish with no designated "homeschool space" so things need to get and stay picked up.
Cassidy, congratulations on striving to meet the autonomy needs of your children. So many parents give in to the knowledge that it would usually be easier (or at least quicker) on one level to just do everything ourselves but that sends our kids the message that they have no worth in our lives and in their home. My dd has been anxious just lately to "be big" and do things on her own, but of course reluctant or downright determined not to clean up. We generally follow the can't get anything new out til the previous activity/craft/game is put away. We also do what StarLynn suggests, clean as you go,(which we call CAYUGA), especially in the kitchen. We just say, and we want to do CAYUGA so we don't leave ourselves a mess at the end. She thinks this is very funny, but perhaps she's easily amused. I do help her to clean up many of her messes, but I DO NOT clean up for her. In other words, if I'm helping and she's distracted and starts playing or lollygagging, I'm done and she knows why. Also,she knows that if things get left lying around, they will "dissapear" for awhile, just like starlyn suggested putting things away in a basket.
I think by six kids need to know about the responsibility of cleaning up their messes and though I'm not a strict mom or super-neat, I am the only one amongst dd's friends whose mom makes them clean as they go or help clean up before the end of the playdate. I expect dd to help her friends clean when she's at their house but those moms don't bother (I expect they end up feeling it's just easier to do it themselves) and I believe we do our children a disservice by this age not to be consistent about encouraging them to take responsibility. They are asking for autonomy; with that comes responsibility and we don't serve them to wait until they're teenagers to begin to expect that from them.