Following an inquiry I recently received, I've been comparing Korandjé data to the Northern Songhay comparative wordlist in Rueck and Christiansen (1999). In the spirit of open data, you can view the wordlist (with a few remaining gaps to be filled) here: Korandjé 380-word list for Northern Songhay lexical comparison. Draft version, 14 July 2014. The results should be treated as provisional, since the Tasawaq part of this wordlist in particular appears a bit unreliable and since a few gaps remain in the Korandjé and even Tadaksahak lists, but are nevertheless interesting.
Counting cognates makes it very clear that Korandjé is the outlier, as might be expected based on geography:
The other three Northern Songhay varieties (treating Tagdal+Tabarog as one variety) form a linkage, which, following Wolff and Alidou's suggestion, we might label Azawagh Songhay - from west to east: Tadaksahak, Tagdal+Tabarog, then Tasawaq. On this wordlist Korandjé is clearly closest to Tasawaq, but that's only because Korandjé and Tasawaq have both kept more Songhay vocabulary, a fact irrelevant for subgrouping. The only innovation in vocabulary that Korandjé and Tasawaq share to the exclusion of the rest is the borrowing of numerals from 5 up from Arabic, and if you look at the sound correspondences it's clear that Tasawaq and Korandjé each borrowed their current numerals separately from different dialects of Arabic. Tadaksahak, Tagdal, and Tabarog all show almost the same number of items shared with Korandjé due to common borrowing from Berber, and most of that is due to shared borrowings of widespread Berber words that could easily have happened independently. The use of a Berber form originally meaning "weaver" for "spider" in Korandjé and Tadaksahak alone is striking, but very likely coincidental.
Another way to look at this is to note that 188 of the 332 items are shared across all of Azawagh Songhay, whereas only 108 are shared across all of Azawagh Songhay plus Korandjé. Of the latter, only 9 are Berber or Arabic loans, while 99 are Songhay retentions:
eye, ear, mouth, head, hair, neck, milk, belly, foot, hand, skin, blood, urine, liver, person, man, woman, owner, name, dog, cow, donkey, (venomous) snake, louse, meat, fat, stick, grass, rope, salt, pot, pit (hole), iron, fire, smoke, ashes, night, sun, day, yesterday, wind, water, stone, one, two, hot, cold, long, old, lots, red, black, white, dry, full, what, where, near, far, and, sit down, stand up, lie down, sleep, bite, eat, drink, suck, laugh, cry, see, hear, know, love, give, steal, hide, give birth, die, kill, walk, run, fall, wash, pierce, hit, tie, do, sew, bury, sandals, horse, truth, falsehood, finish, dig, stand, find.This list is dominated by basic, rarely loaned words: nearly half of it overlaps with the Leipzig-Jakarta list. However, more culturally specific shared retentions such as "iron", "owner", "cow", "donkey", "horse", "pot", "sew", and "sandals" remind us that the split of Northern Songhay is after all rather recent (much more so, in fact, than these words alone might suggest).
These pan-Northern retentions, however, by no means exhaust the Songhay lexicon of Northern Songhay. Korandjé alone retains some 183 list items of Songhay origin, at least 135 of them shared with Tasawaq, while for many words (eg "four", "green"), only Tasawaq has kept Songhay forms. Well over 227 items have Songhay equivalents in at least one Azawagh Songhay variety, and more than 241 have equivalents either in the Azawagh or in Korandje. If the even more conservative (but extinct) Emghedesie variety were added to the list, that number would no doubt be even larger. Proto-Northern Songhay certainly had a significantly larger Songhay lexicon than any of its descendants does.
[Later addendum]: Removing all words with Arabic-derived Korandje forms from the list makes no difference to the classification; the table ends up like this: