I am using a pivot table as an efficient way to aggregate text responses from
a large data set. However, the pivot table cuts off the text after the first
255 characters (similar to when you copy a worksheet by using the move/copy
option).

How can I overcome this? I have tried putting the pivot table on the same
sheet as the dataset, but that does not work.

I should also note that these pivot tables are then fed into an automated
report through a complicated set of VLOOKUPs, etc. The pivot table
aggregates several questions and responses from many areas of the datset into
one discrete, defined area.