After what feels like forever and after asking several questions (like this, this and this), I believe I may have decided upon a suitable orbital system for my world:
$M_{S}=2.272\;571\;144\;5 \times 10^{30} = 1.142\;857$ $\color{blue}{\underline{M_☉}}$
$M_{P}= 1.898\;2 \times 10^{27} = 1 $ $\color{blue}{\underline{M_J}}$
$M_{M}= 2.272\;686\;259\;599\;33 \times 10^{25} = 3.806\;844 $ $\color{blue}{\underline{M_⊕}}$
$D_P = 324,936,410.689\;212 $
$D_M = 14,596,597.842\;622\;8 $
$AD_S \approx 1929\; \mathrm{arcseconds} $
$AD_{P\,min} = 2374.8 \; \mathrm{arcseconds} $
$AD_{P\,max} = 2879.4 \; \mathrm{arcseconds} $
where $M_S$ is the mass of the sun in kilograms; $M_P$ is the mass of the planet my world orbits in kilograms; $M_M$ is the mass of my world (it's an Earth-like moon) in kilograms; $D_P$ is the average distance (semi-major axis) from the planet to the sun in kilometers; $D_M$ is the average distance from the moon to the planet in kilometers; $AD_S$ in the angular diameter of the sun (as viewed from the planet) in arcseconds; $AD_{P\,min}$ is the minimum angular diameter of the planet (as viewed from the moon) in arcseconds; $AD_{P\,max}$ is the maximum angular diameter of the planet (as viewed from the moon) in arcseconds;
One year in my world is defined at the amount of time it takes the Earth-like moon to orbit around the planet, which should be equal to about 360.3126455 real-life Earth days. The amount of time it takes for the planet to orbit around the sun is about 1093.734343 real-life Earth days.
I have calculated the radius of the planet's Hill Sphere in this system as 21217756.17 km, which allows my Earth-like moon to orbit at the desired orbital period and distance.
The problem
My main issue here is the sun. The distance from the planet to the sun is a little further than Mars is to our own sun. If I am not mistaken, under normal circumstances, this would place the planet outside of the habitable zone where life can form.
What kind of sun can have a mass of 1.142 solar masses and have a habitable zone 324,936,410 km away?
For bonus points, I'd like to have my sun have a similar angular diameter when viewed from the planet as our real-life sun, which is approximately 1929 arcseconds.
NOTE: I have re-read this question very carefully to ensure I only use the term 'planet' to refer to the body in direct orbit of the sun. Similarly, 'Earth-like moon' or just 'moon' is used to refer to the main setting of my world, which is actually a moon orbiting a larger Jupiter-like planet.
UPDATE: It might not be possible with these numbers
I'm looking for a habitable zone that is large enough to accommodate the distance between the planet and the moon. So the Earth-like moon should never leave the habitable zone.