The big labs I'm familiar with ran cine processors. They're continuous machines, preloaded with plastic leader material. You start up by tape-splicing the front of the film to the end of the leader. When you run out of film, you attach a roll of leader to the tail end of the film, so the machine automatically restrings itself with leader. Obviously this is only sensible if you have quite a lot of film. Our last machines ran 50 ft/min, so that 250-shot roll would only take about 40 seconds of machine time.
For smaller quantities, there were roller-transport machines, such as the Kodak Versamat. With these, you could attach the front end of a film roll to a stiff plastic card, which then "leads" the film through the processor. This is the same way modern mini-lab processors work. Your film could be essentially any length you want.
I know that large reels were available for manual-type processing, but never worked with that sort of thing (beyond standard Jobos)