So Universe Sandbox has confirmed, as far as I'm going to investigate it, that a hot-Jupiter scenario for my conworld is plausible. The star is about 5% more luminous than the Sun is, and the planet- a gas giant with 1.25 the mass of Jupiter- is at 1.10 AU. As for the "moon", it's about 9000 km in radius and somewhat more massive than the Earth. It has no sub-moon. It's unclear whether you can ever make sub-moons stable.

In several ways, I feel like inhabited moons might be even more plausible than inhabited planets. (They can piggyback off their planets' magnetic fields for protection from the ravages of solar wind, and moons are more common than planets). There's only one issue, though, which is the seasons. If my moon orbits its planet once every five days or so, then its axial procession is relative to the planet, and has nothing to do with seasons. Instead, the planet is going to have a somewhat more eccentric orbit than Earth does, so that the distance from the sun changes enough to affect the climate; "winter" occurs at the aphelion and "summer" at the perihelion. As a corollary, the seasons are world-wide; there's no hemisphere swap, and no area is unscathed.

I suspect this will create several new climate types. For example, tropical lowlands will still have the moderating effects of being in the middle of the planet, so they won't experience really unpredictable heat waves or cold snaps, but they'll still have temperature changes as the year progresses. For example, maybe you'd have a "tropical rainforest" climate that ranges from the lower 70s (lower 20s C) in January to 90 (lower 30s C) in July- a more moderate version of the southern US or China. Other than that, though, I'm not sure what a planet-wide seasonal cycle would do.

(On the other hand, I'm not sure how much of Sandbox's climate simulation to believe. If you give Venus, for example, an Earth-like atmosphere instead of the one it has, add water and give it an Earth-like day, it freezes over.)