Forcing numbers stored as text back to numbers

I've got a whole plethora of worksheets that have COUNT based formulae, operating on a given subset of data that is copied-and-pasted into these worksheets. Unfortunately, an "upgrade" to the system from which that data is copied has changed the primary datapiece to be changed from a number to a number-stored-as-text when I copy stuff in. I'd like the users of my sheets to not have to do the select-and-convert thing every time the use one of my worksheets.

At first, I thought I could get around it by using COUNTA instead of COUNT, but that won't work; I use COUNT to determine when, in a set of numbers, to insert some text, so I really need a way to differentiate thes numbers-stored-as-text from actual text.

Is there some way to force pasted data back to numbers? Or at least treat them as numbers is other places in the worksheet?