Having been through construction of that type myself, I wouldn't bother, other than with the straw (or woodchips) to keep the mud manageable. In the spring, you can till/rake/whatever and add organic material and start planting.

I agree completely. Whatever you do now will be overcome by events as the building construction goes on. Forget about everything for now and let Nature take her course. Then when the construction is finished, look at the damages and see what needs to be done. Chances are you will scrape it entirely again to restore proper surface drainage and prepare the surface for sod or seed. In any case don't rototill to prepare for sod or seed. Real landscapers (the professionals) only work with the surface and never the subsurface. When I was in college I worked for my BIL who was a professional. You don't need to "till (fill in your favorite amendment) in to" the soil. Now that I know a lot more about soil and have been reading the experiences of so many others over the years, I can see the wisdom of the method. Despite what Sunset Magazine has been saying for decades, rototilling is not good preparation for grass. It might work for a veggie garden but not for grass. Work from the surface and things will go much better for you.