Concrete works best if poured into a form, not into a dirt hole. It's also considered a really bad idea to apply a load on concrete before it has cured (about 2 weeks). You might also think about horizontal rebar as the end of the foundation pad that sticks out beyond the edge of the chimney bricks experience torsion stresses, which will crack the slab at the chimney line.
It won't work, no matter how many jacks, fork lifts, or helicopters you use to lift the chimney. The problem is that all those methods create TENSION in the brickwork. Brick is good in compression, but really lousy in tension, especially without any reinforcing rebar or center pipe. As soon as you try to lift the chimney, it's going to crack.
However, even if you manage to excavate some dirt from under the chimney base, you have a precision problem. 0.5" out of 18ft is about
0.13 degrees. How do plan to precisely settle the chimney with that level of precision, and how do you plan to prevent it from leaning into the house and destroying the weather seal? Like I previously mumbled, this thing is going to require some expertise and experience. One mistake and you lose both the chimney and the house.You might want to ask your insurance agent if your homeowners insurance covers such do-it-thyself repairs. Mine requires proof that the work was done by a licensed contractor before State Farm will pay on a claim.
Incidentally, you might want to do some reading on the various proposed solutions for straightening the Leaning Tower of Pisa. They closely parallel your chimney straightening problem. Most of the bad ideas were variations of tension problems along with stress concentration (buckling) problems. The only methods that had a chance of working were based on undermining the tower base, and letting it settle into a lower position. Raising the tower would have broken it.