Need help figuring out how to lower pipe down to fireplace

Well,I will just say this. About the chase. I didn't drop my pipe down. I pushed it though 35'. It worked and is still working. It was a heavy push but we did it.

I used an insulated double-wall rigid liner (i.e. not a class A chimney), which is probably lighter than yours but generally similar. I dropped all 25' of it down from the top, and did it without a helper. My liner is designed to be supported from the top of the chimney, its weight hanging from a friction clamp. I slid the pipe sections through that clamp, loosening and tightening it to control the descent and to stop it so I could rivet on new sections of pipe. I think you could do something similar, but you might have to improvise the clamp out of something like 2x4s and threaded rod.

There are bumps and fasteners at the joints between sections, where it's necessary to open the clamp a lot to get past them. Not wanting to risk dropping the liner, I linked together a couple of large, heavy-duty hose clamps (big box store plumbing section) and tightened them onto the liner a few inches above each joint. The screws on the hose clamps stuck out further than any of the protrusions on the liner so that, when the joint arrived at the main clamp controlling the decent, I could open the main clamp far enough to get past the obstructions, and the hose clamp would stop the fall when it hit the main clamp. (Hoping that's clearer than mud).

You will have to get in the chase one way or other to install the wall brackets. I see you have at least one installed now, I think generally they are required a maximum of 8' apart. Unless the chase gets smaller higher up, it seems like a smaller guy can fit inside and install the pipe.

When I installed my liner from the top down, I took one end of a length of rope and tied to the satellite dish base. Then ran the free end through a section of liner, and tied it off loosely. Add another section of rigid liner, screw them together, let out a little rope to lower it into the chimney, add another section, tie it off, and lather, rinse, repeat. Worked very well.