Solution attached. When seeing the Total column in the output, I did happen to scroll down on the Crosstab tool and see that option. It is odd that when you check Sum only, the column headers are taken verbatim from the selected field. However, if you select Sum and Total Column it sticks the 'Sum_' prefix on column headers. I think it would be preferable to always take the column headers verbatim or have a prefix option so you don't have to undo the alterations made to the names.
Ok, so my approach to this was to point at the mess they'd created and say loudly: "No! No! What have you done?" then made them go and sit in a corner and think about what they've done.
I then resolved the data problem as follows:
I then refused to give them the results until they promised to learn how data should be captured and why.