Scientists have done a lot of thinking in recent decades about the possibility of more or less Earth like life, using liquid water, on very large moons of giant planets in other solar systems.
So a good place to start getting an answer would be scientific papers on the subject.
Like this one:
https://arxiv.org/ftp/arxiv/papers/1209/1209.5323.pdf
And on pages 3 to 4 it discusses the possible mass range for a habitable planet, moon, or other type of world.
A minimum mass of an exomoon is required to drive a magnetic shield on a billion-year timescale (Ms ≳ 0.1M⊕,
Tachinami et al. 2011); to sustain a substantial, long-lived atmosphere (Ms ≳ 0.12M⊕, Williams et al. 1997; Kaltenegger
2000); and to drive tectonic activity (Ms ≳ 0.23M⊕, Williams et al. 1997), which is necessary to maintain plate tectonics and
to support the carbon-silicate cycle. Weak internal dynamos have been detected in Mercury and Ganymede (Kivelson et al.
1996; Gurnett et al. 1996), suggesting that satellite masses > 0.25M⊕ will be adequate for considerations of exomoon
habitability. This lower limit, however, is not a fixed number. Further sources of energy – such as radiogenic and tidal heating, and the effect of a moon’s composition and structure – can alter our limit in either direction. An upper mass limit is
given by the fact that increasing mass leads to high pressures in the moon’s interior, which will increase the mantle viscosity
and depress heat transfer throughout the mantle as well as in the core. Above a critical mass, the dynamo is strongly
suppressed and becomes too weak to generate a magnetic field or sustain plate tectonics. This maximum mass can be placed
around 2M⊕ (Gaidos et al. 2010; Noack & Breuer 2011; Stamenković et al. 2011). Summing up these conditions, we expect
approximately Earth-mass moons to be habitable, and these objects could be detectable with the newly started Hunt for
Exomoons with Kepler (HEK) project (Kipping et al. 2012).
Thus it claims that the upper limit for a habitable world is roughly approximately about 2 times the mass of Earth, which is about the mass you have decided upon for your two moons Castor and Pollux.
So possibly you might want to consider reducing the masses of your moons a tiny little bit incase those calculations are correct and the upper mass limit for a habitable world is approximately 2 times the mass of Earth. On the other hand you did write that your story assumes superhabitability of large terrestrial type planets much larger than Earth.
You write:
Leda and the Twins:
TZ343-B/Leda is the gas giant within the habitable zone that the twin moons orbit, and its mass, radius and gravity are 1.078M♃ / 343M⊕, 1R♃ / 11.210R⊕ & 2.725g / 26.723m/s²
TZ343-B-1/Castor and TZ343-B-2/Pollux are both approximately the same approximate mass, radius and gravity: 2M⊕, 1.202R⊕ & 1.385g / 13.582m/s². They both orbit Leda, and are tidally locked in their orbits; meaning that their orbital periods and diurnal cycles are practically one and the same.
So Leda has 1.078 the mass of Jupiter in 1.0 times the radius and thus volume of Jupiter, and so Leda has 1.078 the average density of Jupiter.
Giant planets much more massive than Jupiter don't get much larger in volume. Instead their increased gravity compresses their matter more and more and they get only a little larger than Jupiter and can even get smaller than Jupiter. I don't know the formula, if any, for calculating the radii of gas giant planets more massive than Jupiter. I hope you have checked to see whether Leda has the correct radius for its mass.
Jupiter has a surface gravity 2.528 that of Earth, and Leda has a surface gravity 2.725 that of Earth, which is that of 1.077 that of Jupiter. According to this online escape velocity calculator:
https://www.omnicalculator.com/physics/escape-velocity
Leda should have an escape velocity of 61.88 kilometers per second, 5.53 that of Earth, while having a surface gravity 2.725 that of Earth. So clearly the surface gravities and the escape velocities of planets do not vary in the same proportion.
The data you give on the twin moons are:
TZ343-B-1/Castor and TZ343-B-2/Pollux are both approximately the same approximate mass, radius and gravity: 2M⊕, 1.202R⊕ & 1.385g / 13.582m/s². They both orbit Leda, and are tidally locked in their orbits; meaning that their orbital periods and diurnal cycles are practically one and the same.
So each of the moons has two times the mass of Earth within 1.202 the radius of Earth and thus 1.7366544 the volume. Thus each moon should have about 1.1516 the average density of Earth.
Of course all large worlds compress the matter inside them. I don't know how to calculate whether your moons have, or less, or the same, average density as they would have if they have twice the mass of Earth and are made of the same mixture of materials Earth is.
The moons Castor and Pollux have twice the mass of Earth and 1.202 times the radius, so their escape velocity should be 14.43 kilometers per second, 1.29 that of Earth. Since their surface gravity is 1.385 that of Earth, this is another example for world builders that surface gravity and escape velocity vary in different proportions and must be calculated separately using different formulas.
You wish to decide:
and the semi-major axes/orbital periods/diurnal cycles of the moons, although Castor should have an orbital period/diurnal cycle somewhere between 20 and 48 hours long.
Since you give the masses of Leda and castor, it is easy to calculate the semi-major axis to go with a specific period.
Using this orbital period calculator:
https://www.omnicalculator.com/physics/orbital-period
I found that an arbitrary semi-major axis of 1,000,000 kilometers gives an orbital period of 6.202 days or 148.84 hours. Trying a semi-major axis of 200,000 kilometers give 13.312 hours. 300,000 kilometers gives 24.456 hours.
To be continued.
