Interesting thought experiment. However,
I am assuming the energy from the beta decay and electron capture don’t matter. Maybe they really do matter, but antimatter energy is cooler.
The reactions actually release more energy than the 1.02 MeV of annihilation, and since charged particles release their energy as they travel through a material, you’re going to capture much of this energy (not the neutrino energy, though) so it turns out this is a bad assumption, given that only 1 in 10^5 decays give you a positron.