The house was built in 1920. I'm about to get a new roof due to hail damage, but need to take care of this chimney problem first. The chimney goes 100% through the roof as opposed to down the side of the house. The fireplace flue goes through it, as well as my HVAC/water heater exhaust.

The chimney appears to be made out of some kind of cement/concrete mix and not brick. I think the mortar lines are fake. I haven't seen any evidence of actual brick.

Its condition is causing it to suck up rain and bring it down into the shared interior wall over the fireplace. (The upslope side of the chimney is essentially part of the interior wall above the fireplace.) I know it isn't the flashing/roof, because the water penetration stopped as soon as I put a tarp over the chimney but left the flashing around the bottom exposed.

It was freshly painted along with the rest of the house about 1 year before I bought it. It has obviously been patched in the past prior to being painted. More of the face bricks would come off if I pull on them. The chimney started deteriorating and leaking within 1 year of ownership.

I've had three different fireplace restoration guys out, so I know what they have to say. I'd like to hear your unbiased opinions.

I plan to sell the house in 3-5 years.

I wonder how long the repair would last if I stripped the paint, scraped all of the loose concrete/cement, patched, sealed, and painted? I doubt the previous painters sealed it or properly prepped for painting, so perhaps it would work this time around.

Tearing it down, installing a b-vent for the HVAC exhaust and then roofing over it would be an option. Still, it is ugly (although not visible from the street, and I hear it can be a turn-off to a have a useless fireplace. But, the fireplace doesn't draft smoke away correctly anyway due to the firebox. It'll burn a fake log, but that's about it.

Stucco has been suggested, as the house itself is stucco. If I go with stucco, is the underlying masonry too far gone to be stable?

If the underlying masonry isn't stable, how about building a frame around it that could tie into the roof, and then stucco that? But should I be concerned about that creating some other issue, such as condensation?

As you can see, I'm pretty stuck.