I'm thinking there's probably no reason to devote time to words and photos explaining how I cheated the yarns into place. They only needed to be moved from a connected corner either right to the next corner or up to the next corner. Moving right was super easy and I got in the habit of pulling the last yo back out of the last dc made and completing that yo with the new color. It drapes a short strand of yarn across the chain 3 space that you'll be crocheting into. So the 3 dc that go into that chain 3 space will cover it up nicely.
I need the yellow and white yarn to move to the right corner of the green square so that it's at the corner to the left of my hook. We'll just drape that yarn across the top of the green square between my just finished green square and the place where the yellow/white yarn is coming from.
To start with, I like to pull the final yo of the last dc out and put the two loops it was pulled through back onto the hook. (That's just a method for changing color so the first stitch in the new color isn't wearing the old color for a hat; the last loop the yarn is pulled through will be the one on top so it might as well be the new color.) You can see the final stitch is shorter because now it's missing that last yo and draw through.
It took me a few tries to figure this out, but I also like to have the old color strand (green here) in front of the work before catching the yellow/white yarn (new color)
and pulling it through the two green loops to (again) finish the last dc of the green square on the right.
The yellow strand in front is across the top of the green block from the last row and the strand further back goes to the skein of yellow/white yarn.
And I've draped the green across the yellow strands. (That's to catch it in the slip stitch coming up; otherwise it will hang from the middle of the green block and on the wrong side when you next need it. This will put it in the corner at least, where it would have been.)
and pull a loop through the chain 3 space
then pull the new loop through the other yellow loop, making a slip stitch that connects the corners of the two green squares.
Begin square as in pattern. Here I've already made the first 3 chains, and am making the dc next to those. The dcs are made through the chain 3 space of the green square and the yellow strand we pulled across the top of that will be trapped in the bottom of the dcs.
1 dc is made and you can see where both the green chain 3 and the yellow strand pulled across it are being covered.
That yellow strand pulled across (many steps back) just needed to be long enough to reach across the green square. No extra slack was needed.
Again, this may be completely obvious to anyone who does any amount of crocheting. It took me some tinkering to figure out because the pattern I was using was designed to make diagonal stripes in one direction. When I got to places where I needed to change direction of the colors to make a diamond I had to improvise and play a bit. If nothing else, when I make this again I'll have step by step notes about exactly how I did it! Hurray for that!