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I think the DE is causing the problem. If I'm reading you right you haven't shaved with the straight. I get irritation from DEs and I know its because they're just not as sharp as I need them to be. I don't get irritation from straights. I'd suggest shaving with the straight making sure it's well sharpened beforehand. Aveeno gel should be fine with them. I use the stuff from time to time and, like all Aveeno products, it works really well.
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You might also want to try cold-water shaving. Many of us prefer it, for a variety of reasons that include reduced skin irritation.