The positive-density conjecture for G-regular primes in primitive residue classes

Let $a$ and $d$ be coprime positive integers, and consider primes in the primitive residue class $a\pmod d$. The G-regular-prime density conjecture. The subset of G-regular primes in this residue class has positive density unless

$$8\mid d\quad\text{and}\quad a\equiv1\pmod 8.$$

This is presented as a consequence of the local G-irregular-prime conjecture. The source gives no resolution.