I was stripping because they were smelling bad and they started to feel rough. I figured there was build-up.
I think I figured out why they weren't rinsing clean, though. We have liquid All F/C for our other clothes and somehow the bottle had leaked (it sits above the washer). When I'd cleaned it up, I didn't get all of the detergent out of the space where the top opens, so some had seeped inside and a few drops were dropping into the washer each time I closed the lid. Once I discovered that and got it cleaned up, they rinsed clean quickly.

Thanks for the advice - now I have a better idea about stripping.