50 to 100 years is likely beyond the operational life of the plastic itself though, so the plastic would be breaking down and then leaching out the components. The plastic on these is not breaking down, if you lose the plasticizer from the finished product, the material left behind loses the characteristics it gained from the plasticizer. That's why I argued it was outgassing excess plasticizer that was never amalgamated into the matrix to begin with, not suffering a breakdown of the material itself which has the plasticizer as an integral component.
Second, I still think what I'm saying about plasticizer loss is still not coming across well. You have to lose a lot of plasticizers before you start seeing effects due to loss of the material. With vintage figures we are still not seeing any major negative facts on the plastic itself due to plasticizer outgassing. So I highly doubt you see any noticeable difference with your pressure test. What I am saying, is that a residue that is formed on the surface of the figure is evidence of some type of outgassing. The most likely additive that I can think of that would out gas is the most volatile. The most volatile additive that I can think of would be the plasticizer.
A tacky figure itself is not necessarily a sign of plastic breakdown, but it shouldn't be ignored. In the case of the battle droids I find it to be slightly disturbing because I know these figures were not tacky, sticky, or oily when I bought them. It's a change that is occurred while I have owned them. Something is leaving this sticky residue behind. Additives are in the plastic for a reason, into something is outgassing it is no longer serving its purpose in the plastic. The long-term prospects of storing plastics for say 50 to 100 years are what I'm concerned about when I talk about plasticizer loss.
LEGO posted a press release a couple years back saying their plasticizers have never been phthalates. They don't use much, but ABS without any plasticizer is too brittle to be used, it's like glass, it is very difficult to survive the molding process.
I assumed Lego bricks didn't have a plasticizer because of the polybutadiene. Polybutadiene is an artificial rubber and has many of the characteristics that a plasticizer would have. I spent 3 and half hours searching for what additives Lego adds to it it's ABS. But couldn't find anything beyond the conform to government safety standards. So I'll stick by my original assumption unless you come up with anything to the contrary.
Some of these were stored in a lightless closet under lots of other stuff, UV exposure was limited to only time in factory and very brief time on shelf at the store, yet they yellowed. In my book, that rules out UV.
So back to the discoloration, your step dad is absolutely right about white being very difficult to get right and keep consistent. I think it's a little hard to absolutely rule out UV exposure unless you've kept your figures in a sealed black container. Many households light sources are capable of putting out small amounts of UV. Also photochemical reactions can happen with lower energy visible light. However in this case I think oxidation is more likely cause. Given what I currently know about the flame retardants, I would say they are your most likely culprit.