I came up with a solution: a clear vinyl bag with all of my contents visible. It would be like a glorified sandwich baggie.
I sewed a vinyl zippered pouch using my walking foot and the vintage bias tape with black loopy loops trim.
And then I got an email from the Army stating we could take purses ...
Just in case, I filled my zippered pouch with everything I would need (cell phone, Lip Shimmer, a tissue pouch and vintage hanky, and some cash that my FIL insisted I would need as he handed me some) and stuck it in a small brown purse. I decided ahead of time that, if needed, I would ditch the brown purse at the security checkpoint. (I didn't need to do that, by the way.) And you know what? It made passing through security a breeze. The man took out the bag, looked at it, put it back in and let me pass through the metal detectors.
(And it turns out I did need money. At the end of the White House tour as we were leaving, I needed a drink of water and bought a $2 bottle of water from a snack vendor.)