So, here's my stopgap solution: Open the dryer, and take out a few of the biggest, bulkiest items. Towels, sweatshirts, and the like. Fold them, and put them away (or just drape them over the banister, for now), then add the new, wet clothes to the remaining already-dry clothes, and dry the whole lot together. I think the new stuff actually dries faster with some dry stuff mixed in, and the previously dried stuff (which had been sitting for who knows how long) get dampened and de-wrinkled. Everybody wins!
*I realize that "Just take the dry stuff out of the dryer and stick it somewhere else temporarily" might seem like a good solution to this dilemma, but in my experience, it's not. When things get taken out of the dryer and aren't immediately folded and put away, they are indistinguishable from dirty clothes. I have rewashed the same clean clothes too many times to see this as a labor-saving tip.