Ordinarily your tilling approach would be wrong. Tilling might work in a veggie garden, but it doesn't work in a lawn.

In your case I would suggest getting some landscapers to come look at it. I realize this is not the cheap way, but from what you have already said, it sounds like you don't know where to start. Let them decide whether you need more soil (you don't) and how to level it. If they want to rototill it, send them on their way and talk to the next one(s). Here's what professionals use to level and profile a lawn to get good drainage.

There is a clinker on the front of the skid steer and a box blade on the back of the tractor. The clinker picks up rocks and the box blade levels and profiles the soil to make it ready for seeding or sodding. Note that all the work is done at the surface and not below.

As for adding more topsoil, if your lot was already graded for drainage before the septic went in, then you do not need more topsoil. Adding more topsoil will only ruin the existing drainage possibly resulting in flood damage to the buildings or your neighbor's buildings. I just bought a house where the previous owner did not realize what he was creating. I am now blessed with a moat when it rains. Whatever soil you have can be fixed AFTER you have grass growing. Get it tested and add whatever amendments they tell you it needs. You would have to do this anyway even if you bought new topsoil. Perhaps the amendments would be different, but not that different.

There is only a couple of inches of soil over my septic tank and I can't get grass to grow; the OP might have the same problem. I don't know what the solution is. For my former house, I use a large slap of bluestone as the septic top and left it bare.