So the GF at the time was not happy I was still living out of landry hampers. I promised here I would do something about it. This is what I did. The top hamper is used for soiled clothes, once it's full you simply remove it and bring it to the landry room. The rest just store clean clothes. Simple and effective.
The hinges and latches are just outdoor gate hardware found at any of the big home improvement stores. The wood is just construction lumber. 4X4 for the frame, 1X6 strapping for the panels, and I think there are some 2X4s and 2X2s for the rails. Overall it took me a weekend and then some. I had to build it in two pieces to get it out of the basement, it is really heavy. I used higher quality hampers that had the regidity needed to be able to slide partially out and not buckle.
Hardest part was figuring out the dimensions. How many 1X6s would be used vs how wide the hampers are.
It's still being used over a year later.