I finally finished the basket I was making for Franny's toys, and it's not even June. I used the tutorial here as a jumping off point, but I changed several things.
1. I pulled the strips of T-shirt, to make them curl into yarn-like tubes. I think they're easier to work with that way, and the edges are rolled to the inside, so they aren't likely to fray.
2. I used a no-sew method to join the ends of the pieces together.
Stack the ends on top of each other, fold over, and cut a small slit in the center of the folded edge.
Unfold, then pull the opposite end of the new piece through both slits.
Pull the end of the "parent" piece through the slit of the "child."
3. I aligned the braids so that the stitches are invisible. I'm right handed and worked from left to right. If you look closely at the direction of the strands in the braid, you can see that they mirror the direction of the thread. That makes it easy to hide the stitches under each section of braid.
4. To start and finish, I tucked the ends of the three strands under sections of braid on the back side. The original tutorial showed tapering the braid to finish, but I didn't like the way that looked.
ETA: I opted to omit the handles. I'm using this as a dog toy basket, so I didn't want to encourage Franny to drag it around the house. I also changed the way I started and finished. I didn't like the way the gradual step-down looked, so I wove the strands from the ends of the braid back into the braid on the coil below, then stitched them into place. Like so.