I have a broody setting on a clutch of eggs. Day 7 for them will be Monday night. I intend to candle tomorrow night b/c it matches my schedule a bit better.
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I did something similar the last time I incubated eggs. I cut lengths of PVC and hot melted them to the egg cartons. I would not be terribly concerned about your hand oils. Just be sure your hands are clean when you handle the eggs.
Is this a home made bator? Have you checked all areas to make sure your temp is consistent? With a thermometer that is calibrated to 100* by using a quality medical grade thermometer as your gold standard?
My bator had a bit of inconsistency, even after working with the fan, vents and air baffles. So, my standard practice is to move eggs around in the cartons so that each egg moves through warm/cool zones every day or two. I also rotate eggs 90* in their cup on a regular basis so they are not always tilting on the same axis.