filter flow and dog hair
I have a 1999 Maytag LAT top loader with matching dryer in my kitchen for most laundry. I keep my GE Filter-Flow (1994) at the garage hook-up for the sheet I keep on top of my bed, where one of the dogs sleeps. Other various sheets and towels used on the dogs are also washed in the filter-flow.
It does filter the hair out, quite well and you can see what it has done, in the Filter-Flow pan. I don't know if DD Kenpools have built-in self cleaning filters like the belt-drives had, that would be another alternate.
Both the GE and the Maytag have entertaining spin/drain to watch.
So I would recommend looking for a Filter-Flow in good condition, there are lots of them here in the used appliances stores.