First of all, not being able to see your particular jobsite makes it
difficult to weigh in on this one. What kind of access is there to this
space?

Based on what you've said, and being a concrete contractor, I cannot
imagine carting in 19 cubic yards of concrete. F.Y.I. - a concrete truck
usually holds 10 cubic yards, so you are looking at 2 truck loads.

It sounds to me like your contractor doesn't have much experience with pump
trucks, especially the cost involved. Using a pump truck does not make the
concrete more difficult to finish, where as taking several hours to cart in
19 yards of concrete will make it much more difficult to place and finish.
The benefit of a pump truck is that the concrete can be placed much faster,
thus giving the finishers much more time to do their job.

Hope this helps.