when I get to the join end, I overlap my binding and get it on the snug side, them mark and sew.
First, I do not press my binding in half to start, but I do press the diagonal seam line where I will be joining at the end (this is the start end that I press). Then I sew my binding on, with a 6" or so tail loose. When I get all the way around, I stop about 12" from where I started (so I've got a 6" tail loose on the end side too).
Then I lay my quilt out (just that spot, I don't move the quilt or leave my machine) and open the binding on the start end and lay it smooth over the quilt with the diagonal folded over, then I do the same with the "end" end and lay it on top of the other and get it a touch snug. I then grab the folded over part and the top and pin it. It does not matter where you pin, it's just to hold it. Then I fold the quilt to bring the two points I stopped sewing together and that gives a lot of slack in the loose binding. Then I smooth the two binding ends together (the pin holds them at the correct length) remove the pin and line up the diagonal press line and sew along it. Open it up, make sure it fits a bit snug, then trim and finger press the seam and finish sewing it up.
Then I flip it and machine sew down the other side. But if you hand sew that is what you'd do.
This way joining binding ends has become a non-event and there is no complicated measuring or any of that goofy-ness.