I suggest you to have a look at compositions and ggtern packages. I am not sure of compositions package however I did remember labelling the points by using ggtern.
This isn't directly answering your question but Design Expert software can make excellent ternary plots (but you have to pay for the software): https://www.statease.com/docs/v11/tutorials/mixture-designs/
I would recommend PAST statistics. It is not an r package though but a standalone and free software, however it can produce such plots easily with some customization options eg. labels.
Did u try ggplot2, and using the label/arrow functions? It is a little bit laborious, but it should work. Anyway, it is much easier to export the plot as a PDF, and open it on Inkscape (for instance) and edit everything you want there, colors, fonts, thickness of lines, sizes of dots, and including labels.