Yeah to do really good wheel building requires the right tools to do it. Fortunately dishing tools aren't very expensive. Do you have an actual truing stand? You don't really need an expensive one to get a wheel true.
You should also do a bounce test. Fully inflate the tire. Then keep your hands close enough to where you can bounce the tire several times all the way around. Then test for truing, dishing, and tension again.
Yeah, really good wheel building requires work and patience. Once you have your wheel right then you can work on the chain alignment.
Are you using a rag joint?