Searched for a long time, gave up and posted a question, and then found the answer in a few minutes. Sorry about that. In case anyone else wants the information, I will provide it. O-rings come in different hardness grades, and I believe the correct one here is 70 Durometer.
#331 (2-1/4" ID x 3/16") -- 2
#232 (2-3/4" ID x 1/8") -- 1
#014 (1/2" ID x 1/16") -- 1
These things are dirt-cheap on Ebay, and for all I know, my local hardware store has them.
The backwash valve is a model 14930 Swimquip. Seems vastly inferior to ball valves, but I am stuck with it.