As my question indicates, what is the most viable dairy alternative from a sustainability perspective (ignoring the importance of nutritional value)? From a life-cycle analysis are some options more environmentally friendly than others?
I would argue that by using non-dairy you are already putting yourself into the top 20% of low impact because any plant based alternative to dairy is significantly better than dairy itself.
As you have pointed out the question of one type of plant over another then becomes quite subjective.
The only other thing you could consider is looking at the attitude of the companies you purchase from; some will be more bothered about sustainability than others. Check the corporate responsibility pages of their websites, ro look at their financial statements to see how they are investing in sustainable practices or mitigation.
I cannot answer the questions completely but I have experience in Coconut cultivation and processing. In our part of the world (Southern part of India), Coconut farming is very sustainable since most of the process is manual and Coconut grows very well here without special care. Extraction of Coconut milk is very labor intensive and uses some machinery. The tricky part is processing the milk so that it can be stored. We haven't quite figured out a way to do it without noticeable change in flavor. South Indian cooking uses freshly squeezed Coconut milk and we rarely use it as a Diary alternative.
Again, this is my personal experience and it completely depends on where you source it from.