Thanks for the input, everyone. Jeffs, I like your suggestion of just taking the tires to the shop and asking if they think it's a problem, rather than going in with the idea that I'm going to complain.
I know that I Flak Jacket tires rather than Armadillos, but it seems that even without protection of the Armadillos, the tires should not be cracking. These are not, I don't believe, normal road cuts from glass. I tried to photograph a section of tire that would give a good indication, but those cracks go all the way around. Unless I was riding through a glass-coated road, I don't think I would get that even of coverage of glass cuts. Plus the cracks along the dynamo track are on the sidewall, where the tire shouldn't be hitting the road anyway. I would have attribute them to the tire not holding up when it flexes.
Anyway, no matter how this goes with the bike shop, I'm going to be getting some better tires.