Given the relatively small size of the mainsprings, and the relative complexity of the associated gearing, and the large balance, I suspect that the most likely explanation is that they were looking for improved accuracy rather than run time. As you say it looks more like their aim was to reduce isochronism errors. Your freshly cleaned version seems to suggest that this might have been a successful engineering endevour.
Compare with for example the double barrel Seiko spring drive.
"This same elite team of watchmakers now presents Caliber 9R02, a new movement that has two mainsprings set in parallel within a single barrel and uses the unique Torque Return System* to deliver a power reserve of 84 hours."
In that particular caliber the setup of the two springs is some what different. I suspect the increased jewel count in the Seiko might be put to a somewhat more productive use too.
Although the Seiko is arguably not fundamentally that much more accurate.
"A new Spring Drive caliber, 9R31, which has the same dual mainspring structure as 9R02 and the same high precision rate of one second a day and delivers a power reserve of 72 hours."
Pivot must be out of jewel hole in the first picture. Let us see a top view of the coil with pivot in jewel hole.
Looks repairable specially if the collet is removable.
Next you may need to detatch the balance complete from the cock. Lets see the coil then.
As for the broken screw, check if any of it sticks out the other end, else you will need some alum.
I thought pretty much the same to start with but the relatively small increase in power reserve (up to 47 hrs according to Ranfft) didn't seem to justify the increase in complexity of design and corresponding increase in manufacturing costs so I did a bit of thinking around the subject.
To be fair the conclusion I came to was in part speculation on my part, but it was also alluded to in a number of the articles that I read at the time, and it does make sense.
Another aspect to consider though is that using two small barrels instead of one larger barrel provides a different set of options regarding how you fit all of the bits into the limited real estate of the base plate, and this may also have been a consideration during the design process.
Absolutely, the hairspring is the most delicate thing in the watch- when it comes to manipulation.
It's unlikely that the hairspring was like that before you removed the balance cock. It simply wouldn't have run. It can't get like that from a drop or even being thrown from a rooftop.
As I understand it, the Chinese movements often leave the factory unlubricated and even with manufacturing debris present. This was probably the cause of stopping.