My drying rack has a mesh section on the top. I also have some drying racks for sweaters - a large square of mesh on 4 short legs about 4 inches high. I have a couple so I can put a sweater on the first one, put a 2nd one on top and then put another sweater on it, and so on. The air circulates above and below each item. You can buy these at places like Bed Bath & Beyond as well as through catalogs. Things dry 3 times faster than laying a sweater on top of the dryer or on a table or towel. If things spin dry or if you hand wash and roll in a towel to squeeze out the excess water, it shouldn't take too long to dry.
I put the "body" of the sweater on the mesh screen, and then fold the sleeves back over rather than let them hang on the floor. "Drying flat" means no wrinkles but it doesn't mean you can fold a sleeve back over onto the sweater.
I would NOT put things in the dryer. That's the whole point of "hand wash, lay flat to dry"!! Use the gentle cycle, not too much soap, and cold water. I've used Dryel too as another poster suggested, but it's not really cleaning things, just freshening them. It's covering up any odors and it's not removing sweat or anything else. If something is clean but just a little musty smelling from being in a dresser all year, it might work. But if the items are actually dirty, Dryel isn't doing a thing except putting chemicals into the mix to give it a new smell.
I don't think there's a real shortcut here. I know you have 12 items, but I think the best you're going to do is 4 loads of 3 things each. In 4 days, you'll be done - and since things have been lying around in your closet for 6 months or more, that's not such a bad deal!