Basically what I have read, at least the way I understand it is as
follows. I need to remove about 6 inches of my clean fill. Then till it
about 5 inches down. Then I should add 5 inches of topsoil plant the
seed and then add 1 inch of mushroom manure.

Does the above paragraph seem accurate?

Not one word seems accurate. You can do all that, but it won't provide any benefits over your current soil. Let's just say you can create an excellent lawn without doing any of that. Furthermore now is not the time to be doing this. If you are serious about having a fairly nice lawn, fall is the time to renovate.

I promise you can grow grass on the soil you have. Unless it has been poisoned, it can be fixed. IF it needs to be fixed you can fix it. If you take out this soil and bring in new soil, it it just as likely to need to be fixed, so you cannot win with new soil.

There are four things that improve your soil. The first is to grow stuff in it and make roots. Grass is good because grass plants discard about 1/3 of their roots every year. These discarded roots become valuable organic matter in your soil. The second thing you can to do help your soil is to not kill the microbes by using fungicides and insecticides all the time. Fungi and microarthropods (invisible insects) are extremely beneficial elements to a healthy soil. A healthy soil will help prevent the need for fungicides and insecticides. The third thing you can do is to get a really good soil test for the chemistry. This is the part where you believe you could improve it with new soil. That may well be, but different soil is not always better. The $25 soil test from Logan Labs is the best in the country. Post the results on this forum and you'll get another $200 of free advice. This will fix the chemistry of your present soil just as well as it would fix any other soil. And the last thing you can do to improve your soil is to water it properly. If you don't do this one, you may as well not do any of the other stuff.

Spring is a bad time to renovate a northern lawn. Why? Because new grass seed cannot develop strong roots to withstand summer heat and water. Second is that spring is the time that crabgrass seed is germinating. When you put down grass seed, the first thing to appear is crabgrass plants. People often mistake the crabgrass as their fescue or Kentucky bluegrass seed and stop watering. This will guarantee you have a full crabgrass lawn by July. But if you renovate in the fall, you can avoid both these problems. I would suggest you put some very cheap seed down ASAP and hope to beat some of the crabgrass. Then if you lose the target grass in the summer, you have not lost much. What you have gained is roots in the ground, water, maybe a soil test, and a full summer of practicing good lawn care. Then in the fall (late August for you), kill everything (twice), clear the dead stuff, level it, seed into the bare soil, roll it down, and water. So in one sentence I have outlined a much easier and more effective way to plant new a new lawn than whatever you're thinking now.

You have obviously done a lot of reading elsewhere. This forum has not advocated rototilling in preparation for a lawn in a looong time. If you look in your local library at the older gardening books, they do not recommend rototilling. I'm not sure what that came from for a lawn, but it is dead wrong. Rototilling guarantees a bumpy soil surface that gets bumpier and bumpier for the next 3 years.

300 sq ft. Spring. W Pa. I'd consider DIY sod install.

Excellent point. Sodding can be done right now with no penalties for spring. Level the surface, put down the sod, walk all over it to make sure the bottom of the sod is touching the top of the soil, and water lightly every day until the roots knit into the surface. Then back off on watering frequency.

thank you for the info. I knew fall was the best time to plant but I thought Spring was ok too. I had originally thought about sod so maybe that would be my best route.

dchall- wound you put down mushroom manure or anything like that before laying down the sod?

Never before. Personally I'm getting less and less enthusiastic about compost. It is the most expensive thing you can put on your lawn. You would be money and performance ahead using organic fertilizer instead.