I always used Ronsonol lighter fluid, you can leave parts in it for days, providing you have a small container with an air tight lid as it evaporates very quick. No parts that have shellac will be harmed in any way.
You are only drilling out the broken bar not the hole, using a smaller drill if careful will not affect the hole so the angle doesn't come into play. I have in the past done many of these and always had a good result.
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.