L.,
I think you should just try washing the jackets in the washer, but wash them with a few other similar size, bulky items. It works just fine. I have never heard of this problem nor have I had the problem. I wash my kids jackets or my winter down parkas and ski jackets with a couple of towels.
I have had an HE machines for 15 years. I bought the Maytag when it first came out in 1999 and have moved a lot and have purchased I think 3 HE machines now. I currently have an LG too.
There are shorter cycles on my machines, for smaller loads or hand washables.
I wonder if you wash extremely large loads, and that's why your cycles are so long? As the machines pre-weigh the loads to determine how much water is needed to wash.
Also, if you still have a problem, you don't need to go to an expensive drycleaner. Ask a neighbor to wash a load or two, or go to a laundromat.I love using laundromats while vacationing. I get all the laundry done in 2 hours flat.