So I understand that the tonnage was see in Aurora is actually the volume of hydrogen that the ship displaces. How do you convert this into metric tons?
Personally, I don't buy that explanation and just use tons as a direct mass measurement in my headcanon. But anyways...
The density of hydrogen at STP (0°, 1 atm) is 0.0899 kg/m^3. So one metric ton of hydrogen thus represents a nominal volume of (1000 kg / 0.0899 kg/m^3) = 11,123 m^3. We might as well round this to ~10,000 m^3 per ton to make estimating easier.
This means that a 1,000-ton ship occupies a volume of ~0.1 km^3, that is to say that a "small" FAC could take the shape of a square prism 1 km x 1 km x 100 m. Your definition of "small" may vary from mine, but in my mind at least this is a tad outside the range I would consider "small".
The actual density would vary quite a lot depending on numerous factors (not the least of which is the number of large, spacious atriums festooned with precious jewels and placed throughout the ship to raise morale and display the wealth of your empire), but since the density of steel is about 8 tons/m^3 a reasonable estimate would be a density of 1 (metric) ton/m^3 (likely a gross overestimate, but it serves our purpose) to account for alternating areas of dense structures and circuitry as well as open areas for crew walkways and such. This implies that a "ton" of spaceship in Aurora equates to ~10,000 metric tons of physical mass, which means that your 1,000-ton "small" FAC actually contains 10,000,000 metric tons of matter, give or take a zero. Again, for a certain definition of "small"...