The misleading label on the modem chassis, "RJ26 lines 1 thru 8", was almost right. The connector was RJ26X, which has well-documented pinouts. My previous searches for "RJ26" or "RJ-26" proved useless, since current search engine technologies apparently won't try to suggest "RJ26X" for "RJ26". I can't really blame them, since it's not a very common term and doesn't resemble anything like natural speech.
This discovery lead to another dilema: each phone line is actually represented three times, each using what appear to be different technologies. The first "Fixed Loss Loop", and second "Programmed register" appear to be special cases, and the third seemed to do what I wanted.
So one of my side projects is about to resurge to the fore. This should be fun.