MJC- Welcome. I am glad you are wanting to go organic.
I am not the expert here ( Paul Wheaton, the administrator is ) but I think that the dolomite has the same effects as lime which is to raise the pH. Your pH is a little low, but not much. I am not sure why they reccomend sulfur because that lowers pH. I say forget about the chemicals ( I think the dolomite is a chemical) and plant your grass seed. I use the Ringer brand fertilizer. It is an organic fertilizer with an initial burst of nitrogen and has some delayed release of nitrogen also. Once your grass reaches its mowing height ( 3-4 inches ) water infrequently and keep mowing high (3-4 inches). http://www.richsoil.com/lawn/index.jsp
This article can tell you more. I am sure others will offer some advice too. There is probably more to do before planting or at least other options. Hopefully Paul Wheaton will be able to get back to you also. He has really helped me a lot. Good luck ! Try not to use chemicals. Nothing good comes from it but bad things do.