  Symbol alphabets of n-particle amplitudes in N=4 super-Yang-Mills theory are
known to contain certain cluster variables of Gr(4,n) as well as certain
algebraic functions of cluster variables. The first paper arXiv:2007.00646 in
this series focused on n=8 algebraic letters. In this paper we show that it is
possible to obtain all rational symbol letters (in fact all cluster variables)
by solving matrix equations of the form C Z = 0 if one allows C to be an
arbitrary cluster parameterization of the top cell of Gr_+(n-4,n).
