I am really tempted to throw them in the washer and dryer but I don't want it to look like I klled a chicken in there.
You can wash them with care. The link below shows how
Here is a link that might be useful: care for down pillows and comforters
It's absolutely OK to home launder your down pillow, but it requires some attention. True, it's a good idea to protect it as best as possible so it doesn't need to be washed that often. I'd suggest the gentle/delicate cycle (not knowing the quality). Importantly, dry it on a low temp and stop and fluff it a few times to remove clumps (some use dryer or tennis balls. Ensure it's completely dry before putting it inside the pillow protector and case.
I have heard that you want to use a laundry soap, not detergent to wash down so you don't remove the natural oils in down. I suggest that you buy a bar of Ivory soap and grate it into a powder with a box grater. Use only about 2 or 3 Tbs. Then you need to be sure not to let it foam too much if you have a front loader. The tinyest smear of any silicone grease on one of the pillows will do that. Wash with as much warm water as you can get your machine to use and wash long enough to get the pillow clean but not tear the stitches on the ticking. I have done this with success in my front loader.
Down does not have any oils natural or otherwise. Feathers do because they were oiled from a gland near the birds tail.
If you have a down and feather pillow your advice may apply but pure down pillows will have no oils.
One reason you wash them is to remove the oils deposited from your head.
oilpainter, I don't really trust your info on down. I have read that it does have natural oil that keeps it strong. When you wash that out it becomes lifeless and tends to clump up according to what I have read. An outdoorsman gave me the tip to use a mild soap instead of detergent. Probably before your day you could buy a product called Ivory Snow that was made for washing dishes and useful for this. Also the competing brand was Lux soap. Neither is available any more alas.