The following notes might help future research.
The site starts behind the drain cover which will be found to the right of a workman's cabin which itself is to the right of the last kiosk for selling postcards and guidebooks as you go up to the Acropolis proper. The hypothetical vertical chimney was probably mounted on the drain cover platform. The sloping channel (the chimney) starts to the right of this platform (electric cables dangle over it at this point) see photo d.and descends at an angle of c. 40 degrees for maybe 20 m however I believe that the lower part may only be left over from some earlier lesser chimney. About 8 m beyond the fig tree there is a more convincing moment for the chimney to descend at a steep angle to the ground 7 to 10 m below. This is where I presume the furnace stood.
The pollution of the Acropolis proper still seems to be untouched inside the north portico of the Erektheon. It seems to point directly at the hypothetical vertical chimney
The whole area between the chimney and the Propylon should be investigated again because it is very likely that all kinds of bronze workings took place in the same vicinity. There are signs of smoke pollution all along the cliff face in this area. they are particularly strong just above the 'roof' of the foundry.
The Foundry Cup might be a deliberate red-herring to divert attention from the real thing which must have been something of an arms industry secret.
Old photographs of the Parthenon should be re-examined in the new light to see if the considerable pollution points towards the hypothetical chimney.
It would be worth running chemical test on the cliff-face and all the fissures and holes in it.
I believe that the chimney dropped down steeply at an angle of 70-80 degrees at the lower end. The point at which this is likely is marked by a rock with a fig tree growing on it. The right-hand surface (furthest from the fig) of the rock needs to be investigated particularly carefully as it is just possible that the remains of brick work may be found on it. 3 m further down is another possible point of steep descent.
On the ground 7 to 10 m below there is a rock that is heavily discoloured (by heat?) which I believe to be the site of the furnace though only excavation can find the furnace for certain.