Any and all suggestions??? I'm going to suggest covering it with an inch (minimum) of mulch and watering it. If you provide the moist conditions and keep the direct sunlight and wind off, nature will regrow the fungi which naturally soften your soil. I'd give it at least a month under mulch. Interestingly you should not have to water it much at all. Water it once for an hour and the mulch will keep the moisture level pretty constant. When you decide the soil is soft enough, sweep the mulch into a flower bed and scatter seed. Roll that seed down with a water fillable roller and start watering it for 10 minutes, 3x per day (breakfast, lunch, and dinner) for 2-3 weeks. The grass should be 80% sprouted by then. Something you should know is that grass seed sprouted in the spring usually is not ready for summer's heat and can die off. Fall is the best time to seed to allow the roots to develop before the heat hits. So seed in a month and plan now to seed again at the end of summer.

You might be the first person on here in years that I would agree had compacted soil. Why? Because cars parked on it. They probably parked on it come rain or shine. Moving heavy things on top of moist soil is how you compact it. Most people just have hard soil at the surface but it still has air capillaries that keep it from getting truly compacted. But once you push the air out of moist soil with heavy things, then it compacts.

If you want turf there, I would suggest you do not rototill at all. You could run an aerator if you think you could get it softer than the soil fungi can (you can't), but not a rototiller. The rototiller fluffs the soil to an uneven depth. It is impossible to hold a bucking, 300-pound machine to an even depth. When the fluffy soil finally settles (3 years later) it settles unevenly leaving you with a bumpy surface. Leave well enough alone and only work with the surface.