DISCLAIMER - I have teen girls helping me with laundry, and I never got my laundry done in a day until about 5 years ago, but you're a lot more organized than I was. Also, I don't have the kids do their own laundry because doing multiple small loads of laundry isn't very cost effective. Everyone helps with the whole, even adult children.
Here's what we do:
On Monday (our laundry day) we all dump our laundry hampers on the landing and sort/put right side out*. I time the event and we see how much faster we can get the job done each week. Ugh. That's tomorrow.
Once we've got our piles; we have different jobs. I usually assign jobs based on ability, gifting, or sin issues. Older kids have multiple jobs.
Sorters - All littles
1. Put all Laundry Right Side**
2. Stain-out Squirter - boys love this one!
3. Wash Load Starter
4. Transfer Loads to Dryer
OR Hang on Line (If hang on line I help.)
5. Folder - ALWAYS Mom because no-one can fold and get the laundry in the right bins.
6. Clean up Laundry Room
7. Iron and put away
8. Match Socks - I used to do it as a group activity timing this also. Now that they're older; I give it to someone who may not be home during our laundry adventure. This way when they're home from work and lounging on the couch; they get a fun surprise.
*I usually have the person who's too lazy to put their clothing right side out for this job. It corrects the problem very quickly. After awhile you can hear them mutter, "How much work does it really take to unroll a sock?" I just laugh.
**Now that my kids are older, I wash and fold weather it's right-sided or not. They're too old to continue to do it. Now they get their laundry back wrong-side out if they gave it to me that way. I only have to invoke this response once a year because they quickly change their habits.
We have three bins: Mom/Dad, Boys, and Girls
(This works since that divides rooms as well.)
We have an extra bin for socks.
I fold & sort right out of the dryer.
This works in well with our method of schooling. We do 15 minute to 1/2 hour increments of each discipline. We can take a 15 minute break to fold and start another load. We do roughly 4-5 loads of laundry with a load of kitchen towels and rags separately. That's all there is to it! The next day, Deanna goes through and cleans the surfaces in the laundry room, swiffers the floor and it's all put away.