But does the matter-antimatter reaction release more energy than is required to produce the antimatter in the first place?
Irrelevant.
But wouldn't that require the quarks and antiquarks to exist in an unbound state for far longer than has ever been observed under laboratory conditions?
Yes.
If sustained hydrogen-hydrogen fusion has never been demonstrated to be a viable energy source in the lab, then why should we believe that sustained quark=antiquark annihilation is any more viable (let alone plausible) if it has never been demonstrated in the lab either?
The problem with Robosteve's idea (it does not quite classify as hypothesis) is not that the reaction is hard to start, as the hydrogen fusion is, but the contrary: quarks and anti-quarks will annihilate each other just by contact, so his Sun model (if you can call it so) would self destruct in a matter of a small fraction of a second (and, by the way, would destroy Earth and all of FE's Cosmos).
By contrast, a hydrogen nucleus has to smash at a very high speed against another to start the fusion process. It is so hard to achieve that even inside the real Sun only a slow burn happens.
The only place where unbound quarks and anti-quarks coexist without annihilating each other is in Robosteve's head. Nobody has ever proposed a set of conditions where this is even remotely possible. The closest thing to it happened during the first fractions of a second of the universe according to the Big Bang theory, and all the anti-matter got annihilated in fractions of a second, and the resulting universe only has matter in a stable state. And not even then does somebody propose a stable object made of unbound quarks and anti-quarks.