I would like to recommend an option where the financial burden of investigating and possibly building such a facility to fall on an outside party capable of doing this investing the initial cost of building it then getting subscription fees from those owners or tenants who would like to be members of the fitness room or club. If on paper there is no business case for it then why do it. My dear wife for example pays $60 per month and walks to the fitness club winter or summer three times a week. The convenience of in building fitness center would be great.
And while we are talking about limited space, it seems to me that some smart buildings have taken advantage of their roof space and made something out of it. Given our location our roof would make an amazing space for many possible ideas including an exercise room.