Update:
I arrived at YYZ to request the TN, took one look at the general CBP preclearance lines and decided that even if I wasn't sure you could do it through the NEXUS line, it was sure worth a shot.
I lined up for the officer that processes the X's and O's. He responded like it was a completely normal thing for me to request. He had me complete the CBP declaration form that you don't need to do for Global Entry (or which is on the kiosk of GE) and sent me to Secondary, with a comment that after I get the TN, I would need to visit the NEXUS office to add the TN to my record.
In Secondary, it was just time, and I had allowed plenty. All of my materials were in order. He took them and had me sit down and wait while who knows what was happening. Eventually enough of that had happened, and an officer took me down a hall to a little room that turned out to just be where I was to pass the fee through the window and get a receipt.
After I had paid the fee, the officer returned my passport, diploma, etc. and made a point to tell me that he had already updated my NEXUS and I should immediately input "Other" (not B1/B2). That was an unexpected benefit of starting in the NEXUS line. If I had lined up in the general population, I might have just assumed it was on me to update the NEXUS people, and the officer might not have known I had a NEXUS to update.
(Even so, I asked if there was no chance another officer would chew me out for not going to the office, and he said no it was done. I think I still will check, however, as several posts upthread refer to miscommunication of that type.)
For all the posts I've read here and there about YYZ CBP TN processing being challenging and obstructive, the whole thing was very reasonable, I thought.