@Nate There's two products you could look at, One being flow fill it's a soupy weak type of concrete more in the lines of mortar and when it is dry you can actually scratch it with you finger but you won't want to for long. But it's main purpose is to fill in areas where lose soil is in need of stabilizing . in your instance to fill in under the bottom when you go to lift that low edge. The second product is grout but probably 4 times the price same basic principle to fill in under the bottom once you lift the low end. Talk to your local concrete company they may have some other ticks up there sleeve I have heard of self leveling concrete but I have never used it.