+1d6 is for the prerequisite, then the prestige class grants +3d6. Optimal scores will have 1d6 before 10th (for "entry" to the prestige class) and +4d6 by 20th.

I am equally capable of extrapolating from 3/4ths BAB, correct.

This SI is low powered. Expect low power scores. Do clever things to boost the power/versatility despite the SI you're mimicking? Get higher power scores. Pretty simple.