Agreed Patrick, very interesting!
To summarize it seems like the best course of action is:
(1) bake the capsules - regardless of age - in a muffle furnace or ideally a vacuum oven at temperatures between 300 and 550 C for several hours.
(2) weigh in the samples as soon as possible using smooth forceps.
(3) place the wrapped samples in a desiccator (or maybe back in the vacuum oven at low temperature?) until loading the autosampler.
As for the blank increasing after baking, John I'm curious about what happened to your capsules between leaving the furnace and entering the autosampler. I can imagine water vapor adsorbing quickly onto the capsules after being moved outside the furnace.
The Brand et al. 2009 paper (RCM 23: 999-1019) mentions flushing the samples with helium for two hours after loading the Zero Blank autosampler. It's anecdotal, but I tried this yesterday and got undetectable (< 50 mV) peaks for my three unfurnaced blanks. Maybe adsorbed water is a bigger problem than oxidation.