@edgarblythe,
Tell them you need an assistant. Give them a list of what needs doing and appeal for their mercy. They actually like the idea because they get to extend their mini-bureaucracy and have more people under their control.
Limp a bit and rub your back with a trace of agony. You're too valuable to lose because of your knowledge of the structures and the social dynamics of the tenants, and your known good and honest service. Hint at retiring.
And if they are thinking of another investment in the same line you could be appointed General Maintenance Supervisor, on account of your trustworthiness and experience, and have an assistant at each site which would, in the nature of things, require an office.
I shouldn't think the maintenance staff of the Empire State Building is smaller than it was when the building started taking money despite the increasing efficiency of our times.