Yeah, they are massively thick. I've got a Bogut/Howard stored with my uncirculated cards, Jameer Exquisite RC (in a screwdown) and another extremely thick card (which I will display in my mail week, in 1 day or 2).
They way I store them is in a pneey sleeve (the slightly bigger sleeve), inside top loaders (again, really thick). The next option I'm looking at is getting a 4-card storage sheet (similar to 9-card, except 2x2), I have some which I am using to store 94/95 UD SE Jumbos, and then storing the UNC or toploaders in one of those.
But awesome mailday.