Don't know if this will work for you, but I saw a "this old house' clip and this is sort of what they said. They first nailed down furring strips, leveled to the finished height. Then you pour the leveler between the strips, and then when that dries you remove the furring and fill it in. I would use a float to make it even since the capillary action can make it want to rise higher than the edges. One caution (from me, not them) - make sure there are no gaps under the strips or the leveler will flow under and it will be a big mess. After writing this, and come to think of it, I'd just nail down furring at the edges (making a form), and pour the stuff in there. Make sure you know what the low spot is, and adjust accordingly. If there are any gaps under the furring, seal with duct tape first. Good luck.

Tough call, if its me, I try grinding that area to lower that rise down to 1/4 in over the 2-3 feet. Since the area is small, I would use an angle grinder with a concrete plate, its very dusty, so be prepared, and use a vac if possible. In my experience with self leveler, it works wonders, but still requires a tad bit of grinding once set up to smooth it out. also seal that crack, and check the moisture reading on the concrete. nows the time to find out if theres moisture issues, before you lay down an expensive floor.

If you're a DIY'er, you can use a self leveling cement on top of your ply subfloor, but you have to install a wire mesh first to act as it's skeleton, insuring it's stability. Remember, all wood moves, that includes your ply subfloor, and if you pour a self leveling cement on top of it, it will certainly fail. So you nail/screw down rows of wire mesh and then you can our your self leveling cement to give you a nice flat subfloor to glue down your parquet. How to achieve a truly flat subfloor/The Flooring Blog

Sure...you can shot blast the surface so that raw/rough concrete is showing. Then you will go ahead and do everything the way it should have been done. That is to say you will prime and then add the expensive microtopping to level the floor. Why microtopping? Because regular slab concrete is not 'good enough' to become a high-end finished concrete floor. A well finished concrete floor (no stain...just microtopped and ground to a polish) is $5-$7/sf (done professionally). If you want a professional to stain it, you can add another $2/sf. If you want a protective coating that will NOT stain nor etch (which all concrete will do) you can add another $2/sf. A clear coat epoxy is a finish that will have very little maintenance. A wax finish will require extensive maintenance (like every 6 months). A regular 'urethane' finish will require maintenance around about year 2...and every 2 years ever after. A temporary polymere finish (6months worth of finish) will require reapplication every 6 months. A stained concrete floor without a finish is going to be very splotchy...even if it didn't start out that way. As upset as you are right now, this might be a blessing in disguise. If you wish to pick another floor, now is a good time. With 6.5 years in the flooring industry, I estimate the average concrete floor will 'live' for 7 years. After that the homeowners become tired of it (either physically tired of standing on it; or psychologically tired of dealing with the look and maintenance) and cover it up. And yes...you should have done all the shot blasting, all the grinding, all the leveling with microtopping before staining. Again, it is because poured concrete is not 'ready' to become a floor. It is ready to be covered by something else...and that something else often includes self leveler or some other form of 'leveling' before any other rigid floor is put down. Carpet and sheet goods are the exceptions.