I've got a lawn, about 50' x 70'. It's more than half weeds, despite
several years of half-hearted spraying and picking. The grade is
wrong; it slopes to the middle of the yard.

So basically I want to start anew. My intended course of action is to
flip over the lawn (after the fall) by shovel to a depth of 8" (so
that no weeds return). Then bring in topsoil and grade. Leave over the
winter for further settling. In the spring, fix any holes caused by
settling and then seed.

Wow. Turning over 3500 square feet with a shovel sounds like an awful
lot of work just to make sure that weeds are gone. You could just as easily
use the chemical of your choice to kill everything, water for a week to see
if any seeds come up, then take care of that. Then add the topsoil,
prepare, and plant.

Don't get me wrong, if you want your yard tilled, by all means, till it -
but if it were me, I'd at least rent a tiller, I wouldn't do it with the
shovel!

steve