Splice new outlet branch in attic
You got the right idea but all those wires and splices in a 4"box will be tough. If there's no slack, the existing cable will only be 2" into the box on each side. Think about using two 4" boxes and connect them together with a 2" nipple or piece of EMT. That will give you plenty of room to work with. You'll be running and splicing 14'2 with ground. Your drawing shows 14'3, I think you mean 14/2 with ground.