The perfect printer stand I found was actually an Ikea product: a
Hemnes two-level bench. It's more like a small coffee table, but it's solid wood (not particle board) and is perfectly sized for 3880s/P800s and at a good working height. The second shelf level is perfect for paper, ink carts, materials, et cetera. I've used this for four years with no trouble at all. Before that, I had the printer on a collapsible table, and it did have some shake, but it never affected the printer negatively.
That said, shake is not too much of a problem for these printers. Even the large wide-roll Epsons have some amount of shake as the carriage moves left and right, though the current chassis have reduced this considerably from "noticeable visually" to "can only feel it slightly."