In the I Can't Believe I Didn't Figure This Out Earlier department, we can now do a load of wash in under an hour.
When M. did her first load of wash in the house, she called me down to take a look at how slowly the washer filled--the water was just dribbling into the washer. I checked both valves for the hoses leading to the washer, and they were completely open, so I shrugged and figured that the steel pipes that feed the washer were clogged from 92 years of buildup (from what I've read, steel pipe has a projected lifespan of 40 years).
For the past few months, M. has worked around this problem by just waiting at least an hour before going back down to move the load into the dryer. And when I did laundry last week, I just headed back upstairs and worked for a while before returning to the wash--no big deal.
So I'm unable to explain to you why I got a bee in my bonnet about this last night. I was in the basement waiting for the glue to dry on some shelves that I was building and I could just hear the washer calling to me, so I grabbed my channel locks and headed over to see what I could find out. First, I detached the hoses from the back on the washer and cleaned out the tiny stainless steel filters just inside of the washer connects, even though they weren't very dirty. This made no difference in the fill rate of the washer, so I reattached the hoses and went back to gluing.
Washer: 2. Me: 0.
After a bit of a rest, I realized that it wouldn't hurt to examine the end of the hoses that attached to the faucet, so I unscrewed it and looked into the end of the hose to discover another filter, and this one was almost completely blocked with calcium and rust buildup. Rinsing didn't help, but soaking the ends in CLR for a few minutes did the trick! The flow was still slightly impeded, but since the hoses were ancient, rubber, and not burst-proof, I picked up two new ones from Home Depot and now the washer fills in under five minutes.
Washer: 0. Me: 1.