Can anyone comment on how much this may have screwed me?
UK JET here.
Even if they chuck your application out, you aren't going to know why. It could be for any reason, maybe one not even related to your word count. Not worth worrying about.
I doubt even 5% of UK graduate applicants would be 'incapable' of this checklist; the employer wouldn't be wasting their time. However, I'm guessing similar programmes have the same checklist. So applicants determined to teach abroad will have the documentation ready anyway and sent to 20 employers, whereas I was particularly interested in this 1 employer.
Dude, the reason they make you do all that stuff prior to the interview is because of the length of time JET takes to get through the application process, they would be cutting it very fine in terms of getting your work visa ready in time for the school semester. You need your references, resume/CV, degree diploma and academic transcripts for your visa as much as you do your initial application.
If they waited until final selection time to starting processing your application for a Certificate of Eligibility, then there's a whole number of factors which could delay the process. It's far safer and easier for you to just do all that shit right at the start, rather than rushing to do it right at the end.
There are aspects about JET which are a major pain the arse and downright silly, but simply selecting to print four copies instead one is not one of them. If you somehow manage to screw that up or throw a wobbler about it, then it makes it far easier for JET to decide to not sponsor your visa, which is ultimately what you need them for the most. It's not like they need the applicants.