(Note this answer cannot answer the 'maximum people per square foot/meter of living space', but presents a more general bit of useful information concerning the variation of population typically found within a historical household or family.)
Historical demographics rely on various means to be able to estimate historical populations within cites. Direct census type information is rarely available, so individuals trying to calculate a cities population at a given point in history often need to collect examples of information they can find, and then create reasonable formulas to enable population estimates to be made when they find such data, or to enable validation of other historical data encountered.
One epic study (representing 30 years worth of research) can be found in Chandler and Fox, 3000 years of urban growth. (If you have an interest in medieval demographics, this should be your bible.) On page 6 in the opening chapter is a table which represents the relevant types of data this study uncovered on the typical number of inhabitants at various locations and times:
You can see the various data that was collected was from different sources which included counts of households, houses, taxpayer or families. Every source for each cities' information is detailed in the book.
So in comparison to your opening statistics of 2.58 to 5.9 people per household, actual data on late medieval to early modern era populations typically shows values above that. Chandler states that Genoa was the densest city in Europe, and he shows a population of 15 people per house in 1460, well above the 5.79 from the opening numbers.
Chandlers population density for Genoa is listed as over 600 people per hectare (abt. 243 people per acre.) We can compare this with modern density figures for Manhattan of 74,780.7/sq mi (28,873.0/km2) which equals roughly 116 people per acre (288 per ha). So Genoa in 1460 was more than twice as densely populated as Manhattan is today.
So, did people in the past 'live more densely' than today? It varied by circumstance, but there were definitely locations where the population was much more dense than today.
(Note Chandler and Fox must be borrowed with login to access the full text.)