Hm, I'd also perhaps suggest a way to actually see what your gift is without having to put down the chest, kind of like a gift preview. You could then decide whether you cared enough to get the gift or whether it's worth removing things out of your inventory to collect it right now.
If you didn't want the gift you could then perhaps /gift remove or something like that. I've been thinking it's kind of annoying to not know what you're going to get and having no way to remove your gift except by collecting it.