I own a pair of the Lunarglide too and I tend to supinate too. I didn't know this when I bought the shoes but they are not neutral shoes (the shopguy told me that they have a pronation control that only comes into play IF you overpronate and doesn't affect you if you don't because they "adjust" to the runner. I think it's just marketing...).
They force me to run on the outside of my foot even more (you can also see this if you look at the shoe from behind. The soles are higher on the inside), I think they are not suited for supinators, who should really look for a neutral shoe.

I never had any issues with foot pain like you, though. I think swelling and severe pain have to have another reason than just the shoe.