We sent the old clock out for repair and have been told a failed Quartz conversion had been attempted in the past, and therefore the clock is current not repairable.
This is mighty peculiar. A "failed" quartz conversion? A quartz conversion on these clocks basically removes all the insides completely, saving the case, the hands, the face and bezel. The "outsides" as it were. Then inside the now completely empty case, they place a quartz movement. These movements are made by the millions and placed in all kinds of things; I cannot tell you how may decorative clocks I've had around my home all with the same movement in them. In the case of the Pagoda clock, it's not the same as these, but a smaller movement.
The two better known places for quartz conversion would be North Hollywood Speedometer
https://www.nhspeedometer.com and Palo Alto Speedometer
http://www.paspeedo.com. Others you may try include Seattle Speedometer
http://seattlespeedometer.com Southern Electronics
https://www.instrumentclusters.com/clock-repair. There are probably some others out there as well.
There are two distinct camps here; the absolute purists who will live with the inherent and incurable inaccuracy of the original clock (a Rube Goldberg contraption if there ever was one) so they can listen to the mechanical noise it makes as it is electronically wound now and then (without caring whether or not it's ever accurate) and claim originality, and those who have converted theirs to quartz.
Though it was a different time and space, I converted mine (Palo Alto did the work) back in 1999-2000 and it's kept perfect time since then. I did this upon the recommendation of Palo Alto. Even then they had determined that trying to make these clocks work (new Pagoda owners had the audacity to expect the restored and "working" clocks to actually keep time; too many callbacks I guess) was a fool's errand. I delivered a box full of nasty looking instruments to them, and they returned the set six weeks later looking brand new. Have not worried about the clock in the past two decades and all the other instruments have been fine as well.
It may be difficult to find someone who will actually work on the original clock and attempt functional restoration for you. If they do, don't expect it to keep time accurately...
PS: For those too young to remember, or perhaps non-Americans, Rube Goldberg is known for his cartoons that depict very complicated gadgets and machinery performing very simple tasks in indirect, complex, Byzantine ways. The cartoons created the term "Rube Goldberg machines" to describe related gadgets and processes...and the Kienzle clock for the Pagoda is one such example.