Or, rather, tried to call. Instead of going through the pile of tax documents for account numbers impossibly long, I took a chance on getting a sweet operator.
Today I got an an agent named "Sandy" with a real sweet Rochester accent and nicely cultured voice. She did it from my social security number, found my sister and her husband's account right off, and could tell the right account from "It's the ones with all the (first number that recurs frequently in their account)'s, (second recurring number)'s and (third recurring number, removed for safety's sake)'s. The two account numbers are different enough that it stands out," I explained.
She agreed, and put $53 from my checking to theirs.
Thought she'd get a kick out of that transaction, one of the weirder I've had for a while. Super bank people.