Here's a slightly different diagramslightly different diagram from the usual chart for atmospheric escape, just for variety. You can see that Mars is right at the lower limit for the Mass required to retain an N2 atmosphere. It is also dense enough, at ~3900 kg/m3 to be safe from destruction by tidal forces. Unlike the real-life Mars, a Mars moon snuggled up to a gas giant is safe in its parent's protective magnetosphere and so should hang on to much more gas for much longer.
Note that this is now right on the edge of plausibility. Long term stability of the moon's orbit is dubious, and were Jupiter close enough to the Sun for the moon to be within the habitable zone the additional heat input from solar irradiance would warm the gas giant and inflate its atmosphere, and your low-altitude moon would likely be dragged down into the atmosphere in a relatively short period of time. Because the precise relationship between atmospheric height of a gas giant and surface temperature isn't trivial to pin down, this could be handwaved as having a less-massy giant than Jupiter which has expanded to the same size in the heat... this would of course affect things like orbital period, but as you've not asked about that in your question it does not need to affect the answer in the slightest.
All that needs to be done is to keep the exobase of the moon's atmosphere clear of the gas giant's exobase, to prevent any drag or atmosphere-stripping problems.
Here's a slightly different diagram from the usual chart for atmospheric escape, just for variety. You can see that Mars is right at the lower limit for the Mass required to retain an N2 atmosphere. It is also dense enough, at ~3900 kg/m3 to be safe from destruction by tidal forces. Unlike the real-life Mars, a Mars moon snuggled up to a gas giant is safe in its parent's protective magnetosphere and so should hang on to much more gas for much longer.
The scale height of a Martian atmosphere with an Earthlike average atmospheric temperature of 287K is defined as $H = \frac{k_BT}{mg}$ where $k_B$ is Boltzmann's constant, $T$ is 287K, $m$ is the mass per molecule of the atmosphere (4.65x10-26 kg for N2) and $g$ is the surface acceleration due to gravity, which for Mars is ~3.7m/s2. $H$ is therefore ~22.9 km, not far off Jupiter's own. Earth's scale height is about 8.5 km, and its exobase is ~500 km. Given the same proportions, the Mars-moon's exobase would start at ~58.8 times its scale height, or ~1350 km. In practise you could get away with a lower surface pressure than Earth for a reduced exobase altitude, but this is an adequate start.
Your minimum altitude therefore becomes 2300 km (for the parent's exobase) + 3400 km (for the moon's radius) + 1350 km (for the moon's exobase) or ~5720 km, giving a rather smaller but still quite dramatic Jovian angular diameter of 81°.
Note that this is now right on the edge of plausibility. Long term stability of the moon's orbit is dubious, and were Jupiter close enough to the Sun for the moon to be within the habitable zone the additional heat input from solar irradiance would warm the gas giant and inflate its atmosphere, and your low-altitude moon would likely be dragged down into the atmosphere in a relatively short period of time.
All that needs to be done is to keep the exobase of the moon's atmosphere clear of the gas giant's exobase, to prevent any drag or atmosphere-stripping problems.
Note that this is now right on the edge of plausibility. Long term stability of the moon's orbit is dubious, and were Jupiter close enough to the Sun for the moon to be within the habitable zone the additional heat input from solar irradiance would warm the gas giant and inflate its atmosphere, and your low-altitude moon would likely be dragged down into the atmosphere in a relatively short period of time. Because the precise relationship between atmospheric height of a gas giant and surface temperature isn't trivial to pin down, this could be handwaved as having a less-massy giant than Jupiter which has expanded to the same size in the heat... this would of course affect things like orbital period, but as you've not asked about that in your question it does not need to affect the answer in the slightest.
All that needs to be done is to keep the exobase of the moon's atmosphere clear of the gas giant's exobase, to prevent any drag or atmosphere-stripping problems.
Here's a slightly different diagram from the usual chart for atmospheric escape, just for variety. You can see that Mars is right at the lower limit for the Mass required to retain an N2 atmosphere. It is also dense enough, at ~3900 kg/m3 to be safe from destruction by tidal forces. Unlike the real-life Mars, a Mars moon snuggled up to a gas giant is safe in its parent's protective magnetosphere and so should hang on to much more gas for much longer.
The scale height of a Martian atmosphere with an Earthlike average atmospheric temperature of 287K is defined as $H = \frac{k_BT}{mg}$ where $k_B$ is Boltzmann's constant, $T$ is 287K, $m$ is the mass per molecule of the atmosphere (4.65x10-26 kg for N2) and $g$ is the surface acceleration due to gravity, which for Mars is ~3.7m/s2. $H$ is therefore ~22.9 km, not far off Jupiter's own. Earth's scale height is about 8.5 km, and its exobase is ~500 km. Given the same proportions, the Mars-moon's exobase would start at ~58.8 times its scale height, or ~1350 km. In practise you could get away with a lower surface pressure than Earth for a reduced exobase altitude, but this is an adequate start.
Your minimum altitude therefore becomes 2300 km (for the parent's exobase) + 3400 km (for the moon's radius) + 1350 km (for the moon's exobase) or ~5720 km, giving a rather smaller but still quite dramatic Jovian angular diameter of 81°.