When I woke up this morning, the forecast proved true - it was sunny outside, which is a change from all the rain we've been having up here. Either way, I didn't want to lose any time (I knew it was supposed to start clouding up in the early afternoon), so I grabbed the foam roller and started staining the wood.
After a few hours of it "cooking" in bright sun and light winds, the piece felt pretty dry to the touch, so I decided to polyurethane it. Sure enough, by the time I'd finished the work and it was dry enough to move, it clouded up so much I was sure it was going to rain!
The piece is now sitting in the downstairs front hallway until the closet is fixed up. It makes sense to keep it downstairs for now, otherwise it'll be under foot while the quick construction project's being done. In a bit I'll head out to Lowes or Home Depot and see what I can find for hardware for this piece (and see what I can get in terms of wood to replace the shelves). My mind's eye keeps seeing this as a woman's room, and therefore making high heel shoe drawer pulls, but I can't say the next owner would want that, so I have to stay neutral.