_{NOTE: If there is anything about this question that needs clarification or editing, please don't hesitate to let me know in the comments.}

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Get ready, because you're in for quite a ride.

I have tried asking various questions based on different criteria, and I'm finally at my wits' end. In my (hopefully) last question about my solar system, I am providing the bare minimum constraints.

In my system, there is:

• A central star
• A gas giant orbiting the star
• An Earth-like moon orbiting the gas giant
• A sub-satellite orbiting the Earth-like moon

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And here is what I am looking for:

• As viewed from the Earth-like moon; the star, the gas giant, and the sub-satellite have angular diameters of around 0.5 degrees. The gas giant may appear slightly larger. This means there are two types of solar eclipse: one where the gas giant moves in front of the sun, and one where the sub-satellite moves in front of the sun. There will also be an eclipse where the sub-satellite moves in front of the gas giant.
• The Earth-like moon is essentially an Earth clone; Earth-like habitability, surface gravity, seasons, atmospheric conditions, temperature, weather patterns, tidal forces, etc.
• The system must have been stable long enough for life to form on the Earth-like moon

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Here are optional criteria that I would like to have, but I realize it might not be possible:

• The Earth-like moon has a cycle of seasons lasting 360 real-life days. This does not necessarily mean it orbits the gas giant in 360 days, it just means that winter, spring, summer, autumn last about 360 real-life days. (Earth-like seasons)
• The sub-satellite orbits the Earth-like moon in about 30 real-life days.

At this point, having asked so many questions trying to figure this all out, my only remaining question is this:

Are there any systems that will meet all of the above criteria?

Or should I just give up and cry?

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What I am looking for in an answer:

• I'm looking for someone to actually help me find reasonable numbers for this system. I am looking for a hard-science answer.
• If there is a range of numbers that will work, please specify that and give me enough detail so that I may calculate or choose a suitable system for my world.
• Please do not say "it won't work" without explaining why it won't work. Also include the calculations you used that determine it is not possible.
• The more detail you provide in your answer, the better the answer is

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Here's what can be changed, if necessary:

• If the tidal forces from a gas giant are too great, the mass and composition of the planet can be changed as long as it allows for the Earth-like moon to be Earth-like and have its own sub-satellite.
• If there is anything else that might need to be tweaked, please provide details in the answer. For example, if the angular diameter of the sun would need to be smaller (due to a greater distance from sun needed for orbital stability) in order to meet most of the criteria.

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Some calculations I did to get you started

The smallest mass of a gas "giant" is around 6 Earth masses (a mini-Neptune), and the largest mass possible is 13 Jupiter masses (at which point it becomes a brown dwarf)

Looking at the planets in our solar system, the densities of the gas and ice giants are measured as being anywhere from 0.6 to 1.6 g/cm³.

With 6 Earth masses and a density of 1.6 g/cm³ (the smallest volume possible), the Earth-like moon would orbit at a distance of 4,025,050 km, having a period of 379 days.

With 13 Jupiter masses and a density of 0.6 g/cm³ (the largest volume possible), the Earth-like moon would orbit at a distance of 49,289,755 km, having a period of 620 days.

Increasing the angular diameter from 0.5 to 0.6 degrees, this changes the above two scenarios in the following way:

• Smallest Volume: Distance = 33,57,127 km, Period = 289 days
• Largest Volume: Distance = 41,110,541 km, Period = 472 days

Based on these calculations, it may be necessary to increase the angular diameter of the gas giant slightly.

NOTE: The mass and density allow me to calculate the volume, which allows me to calculate the actual diameter. From there, using the angular diameter I am able to calculate the distance, and then the orbital period.

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Finally, here is a diagram I made in MS Paint:

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If you would like to see my previous questions that are related, in order to gain more perspective on the matter (they also include the desired mass numbers, orbital configurations, and more) I have listed them here in chronological order:

1. Stabilizing Synchronized Orbit
2. Can planetary bodies have a second axis of rotation?
3. How can I have an Earth-like moon?
4. What kind of star will work for my system?