Adventures in Masonry

I've had a leak in the roof for quite some time. I've tried caulking what seemed like holes and tried tarring over potential leaks. Those tactics seemed to work at first, but soon I saw that I was just kidding myself.
The drip seemed to be about where the chimney is. I reached the conclusion that the water was getting between the bricks and trickling down to where it could drip on the first floor ceiling. The obvious solution is to repoint the bricks. I got on the roof just after noon and attacked the mortar with a trowel. It quickly became apparent that there were three generations of repair jobs and I'm the fourth.
There's the original 1890 mortar which has turned into beach sand. By clearing this away I was able to see light clear through the chimney in many places.
In some places there's mortar from another repointing. This is still pretty intact which just makes removing it harder. It's a 1/4" to 1/2" layer sandwiching in the sand.
Then there's the tar over the lower third of my half of the chimney and over most of the neighbor's half. The tar actually comes in handy in taking down multiple bricks at at time.
The top two layers are pretty solid. I wound up starting 4-5 bricks down and started pulling stuff out from there. This gave me an opening to dig out the sand and pop out the newer mortar. With the top undermined some of it came down, but several still refuse to move.
I came down around 2:30 with most of the chimney in pieces.

Now I have to figure out how to approach this next. How tall should I make the chimney? As tall as it was? It's not like I have a fireplace. Close it off three bricks up? Should I wait until I can order a new roof antenna and built it into the chimney? It'll be cold by then. I should do this now.
I'm gonna spend the next half hour or more just cleaning all the dust off the bricks so I can secure them.
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Another two and a half hours later:
I put the first layer of bricks back in place and repointed the inside of the chimney just as far down as I could reach.
I have a small trough to mix mortar in. It gets about two bricks worth before needing to be refilled. It's amazing how fast that stuff goes from being too thick to too thin.
I'll be back up there tomorrow. About 1/3 of what I took down came off in one big lump. I think I'll repoint that separately and put it back up whole.