It seems you have covered your bases on environment - and newspaper is very safe. I used crushed walnut for a long time and the corn cob stuff before that. Those can actually pose a problem if a bird ingests it and it causes a blockage in the GI tract- so newspaper is definitely the best way to go.
The symptoms you describe sound as though the birds were low on electrolytes - usually a secondary symptom to an illness, injury or toxin. You mentioned that you were using the societies as "nannies" and one was on eggs... you may have a vitamin D3 and/or calcium deficiency. Whether laying eggs or raising babies, your finches are putting alot of energy into their work and societies will often work themselves to the point of illness and death. I use a product called "Calciboost" (you can find it at
www.birds2grow.com). I don't know what types of daily vitamins/supplements you use, but they may need more than a general vitamin regimen during times when they are working extra hard. I know my foster finches are very tired at times, and this with me helping them out on the feeding. I have found that providing fresh hard boiled egg mixed with a powdered eggfood base daily has really helped my birds perk up when they are otherwise fatigued. I chop it up - the entire egg with shell, and then put whatever amount they seem to eat mixed together with the eggfood for a nice soft-food mixture high in protein, calcium and vitamin D3.
It sounds like you have chosen the hardier Aussie finches for your aviary, so you are not as likely to encounter problems such as this very often. I breed and keep some African waxbills which require high maintenance and TONS of fresh live food in order to get them to even try to raise their young. The Africans err on the side of precaution and will toss the babies if they do not feel like they have enough food to share. My two female "foster" society finches seem to be the opposite and definitely put alot of effort into laying infertile eggs between cordon babies. Even though the societies do not have the insect/high protein diet as a general "need," I have found that mine are happy to eat the higher protein foods that I feed my cordons. No feathers go missing and they seem quite robust with the softfood added to the rest of their diet.
One more idea that has worked well for me in the past and still seems to hold true - providing a separate bowl of gatorade (refresh daily) really works well for the healthy birds. They will choose to drink from it when they sense the need. In times of sickness, I always remove all water sources except for the gatorade, confine the bird(s) to a small "hospital" cage, use seeds for the bedding, provide lots of millet, and put a ceramic heat emitter over part of the cage so that the bird can choose the best temperature for comfort. I have had some "no chance" situations work out fine using that set-up.
Anywayz - Good luck and if you have anything I can maybe help you with, feel free to email me personally (email listed below). Hope this info gets to you with no further loss of birds. I am so sorry for the ones that did not make it. I know its really hard no matter how many we have.