I love the quote:
Asked why the problem had not been fixed, Mr. Killion said, “Believe me, if there’s a way to do it, we’d do it. Maybe there’s a way out there we don’t know about.”
If your limit is x,y space, then any "x number of words" limit will, by definition, not match up to reality some fraction of the time.
One thing that they could do is switch to a monospace font for the text box, then at least they could specify a fixed number of characters. Now that I think about it, that wouldn't necessarily work either, because of word wrapping.
The best case would probably be to tweak the font size to allow a fixed number of words to fit in the box.
Alternatively, like you said, you could figure out the necessary font-size based on the word-count, length, or even client's sizing information.
Or like you said, offer logic to have additional pages printed if needed.
Python solution: def under_the_limit(response): return len(response.split()) <= 150
They need to check that, once typeset on the printable form, the text fits in a box of a certain size.
Still, whatever they are using to typeset the form should be able to easily give them that info. Even if, god forbid, they are doing it with HTML they can get that info.
Much simpler would be to design the form with a monospaced font for the essay. This is a big reason why manuscripts are still submitted in Courier even though few people use typewriters anymore.