After getting the go-ahead from our landlord ("Sounds like you guys know more about the machine than most."), Brit and I took to our washer with screwdrivers, pliers, and a hammer tonight to figure out why it wouldn't drain (likely culprit: hair).
Before we got that far, though, we poured ourselves some drinks.
The repair video makes this job seem straightforward enough, but we didn't replace the drain pump. We unhooked all the same stuff, then completely took out the black rubber drain boot to clean it out. I'm getting ahead of myself--making it to the point of unhooking and cleaning out took several hours. First, there was the problem of moving the washing machine out of the laundry room while keeping the dryer (which sits on top of the washer) inside, where it needed to stay connected to the gas line and vent hose. That took several tricky maneuvers and a phone-a-friend to Becca for some extra help in lifting/balancing/shifting.
Then we got down to taking the thing apart. One stripped screw and another phone-a-friend to Jesus for heavy duty pliers later, and we were in. We muscled the clamps off and pulled out the drain. Now, just so everyone is aware, as we disconnected the hoses, residual water leaked out. Not clean, fresh water. Old, musty, dank water. Our work space started to smell like 100-yr old fart. And as we took out the rubber boot, we saw something floating inside. It looked like a rolled up piece of plastic, but upon further inspection (pulling it out with the pliers), we found out what was keeping our washing machine from draining:
One bra cup lining (perhaps from a swimsuit?), several bobby pins...and of course some hair/lint combo clumps. A little gross, but also validating--if the drain had been clean, I don't know what our next course of action would have been. As it was, we spent some time running bleach water through all the hoses we could reach, and thoroughly scrubbed/soaked the drain/drain trap.
Putting it all back together went a little quicker and for our first test run, we threw in all the nasty rags we had just used to mop up fart water. Forty-one minutes later (aka 2 minutes ago) and...success! I just took out a load of clean, fully spun rags from our "new" washer. Brit and I will now curtsy/pat ourselves on the back while you cheer and bravo.