I'm guessing the Purex doesn't work so well for sink washing? I tried (and liked) them a little while ago but feel like the heat and agitation of the washer was what would get the soap out of the cloth thing, so it might not do anything if you put it in the sink. If it does work, that could be a perfect option!
I've also seen laundry soap sheets around somewhere, although I've never tried them. Might get some and try for sink washing.
I guess my standards are low, since I tend to just use hotel shampoo on my ex officio underwear and that seems ok to me.