I'm pretty sure you don't mean a backhoe. A backhoe is an articulated shovel attached to the front of a tractor. What they use to level soil for landscaping is called a box blade. A box blade looks like a hoe and fits on the back of the tractor so join us in the confusion about agricultural and construction terminology. We get the point.

The weight of the tractor is perfect for compressing the soil. Of course nothing will replace the tens of thousands of stampeding bison which were responsible for hundreds of thousands of years of development of the Great Plains. However, the footprint of the tractor tires is roughly the same as bison (minus the stampede) as is the footprint of nearly every animal on Earth.

Measuring soil firmness is beyond practical application. You would have to be able to measure the firmness of everything ranging from chipped pea gravel (rock solid under all conditions) and round pea gravel (relatively slippery upon itself and when in sand-sized grains, the basis for quicksand) on over to pure clay (brick-like hardness when dry and mushy when wet) and pure organic material (surprisingly firm when wet or dry).

Back to seeding. You picked the wrong time of year to do this, but what's done is done. Plan now to have a lot of weeds in August and further plan to reseed properly in the fall. Hydroseeding can work, but I see too often where they don't use enough seed and it comes in thin. That will make the summer weed problem worse. Since your soil is ready now, time is of the essence.

Your soil is properly prepared and ready to go. All you have to do is scatter the seed and ROLL it down to ensure you have good soil-to-seed contact. At this time of year I would use a mix of TTTF seed and use twice as much as recommended on the bag. Use the most expensive seed you can find with zero (0.00, ZERO!) weed seed in it. You will have enough of a weed problem without applying extra seed. After you scatter the seed, rent a water fillable roller to roll the seed down. The proper weight of the roller is when you can walk behind it and your foot prints do not compress the soil any further than the roller compresses it.

There are several ways to get a more even distribution of seed than scattering it by hand. You can use a broadcast type spreader or you can mix the seed into sand and spread it in a drop spreader.

After the seed is down, you have to keep it moist until it both germinates and the roots get established. Water it twice a day for 10-15 minutes for two weeks. After two weeks you can start to skip days of watering. Keep an eye on it but you eventually want to work you way toward watering only once weekly during the hottest heat of summer and less often the rest of the year. The deep, infrequent watering where the soil surface dries out between waterings is what is going to keep your lawn relatively free of weeds. If you reseed in the fall, you will find that you have hardly any weeds next August (2008).

Take this opportunity to raise your mower to the highest setting. When the grass is about an inch taller than the highest setting, you can start to mow. Mulch mow so the clippings stay on the grass. Continue to mow at the highest setting until the day before you want to reseed in the fall. Tall grass is healthier, keeps weeds out better, and holds more moisture with deeper roots and cooler soil.

After the second mowing, the roots are strong enough to take a chemical fertilizer if you want to do that. If you want to use an organic fertilizer, you can start with alfalfa meal or pellets immediately (even before you seed) at a rate of 10-20 pounds per 1,000 square feet.

Thanks dchall for the thorough answer! I wish I could have put this off to do a fall planting, but I lost two trees from a storm last November and the contractor that mid December removed the trees and did the fill work as well.