You're not wrong. The current state of the art puts the precomputation step at complexity L_n(1/3, 1.923)§, and additional individual discrete logs at L_n(1/3, 1.232). So individual logarithms are still subexponential and nothing to scoff at, but they do become easier, yes.

Ignoring constant factors, for a 1536-bit prime this would mean cost ~2^102 for the initial precomputation, and ~2^66 for each individual log.

§ L_n(a, c) is the usual exp(c(1 + o(1)) (log n)^a (loglog n)^(1-a)).