Thanks for those pointers @John – fyi the nLab page says the fact we can derive \$$\lambda_I = \rho_I\$$ from the pentagon and triangle was first proved by Kelly in this 1964 paper:

> [On MacLane's conditions for coherence of natural associativities, commutativities, etc](https://www.sciencedirect.com/science/article/pii/0021869364900183)

I've tried working through the proof of the coherence theorem several times but without success. I'll have another go using that nLab page which might offer some clues about the bits I got stuck on.