He does not answer the concern, he just throws down absolute value bars to make all inertia work the same way.
There is no known and studied behavior of objects with negative mass. There isn't even a rationale for throwing down absolute-value bars beyond "symmetry".
You have it backwards - you can justify throwing absolute value into the equation if you actually find find evidence that negative mass is just as hard to accelerate as positive mass.
I agree that the burden of proof is on him or anyone who wants to run with the idea, but for now its just being proposed as neat, possible idea.
You're reading a speculative blog entry as if it were a rigorous scientific paper and then claiming that he hasn't done the science.
And when someone starts telling stories about a "well-known astronomer" who has substantiated his hypothesis, he's taken his claim to a higher level than "a neat, possible idea".