Big shout out to nihonhacks.com for pointing me in the direction of past exam papers for the Japanese Language Proficiency Test.
Here you can download past papers for all levels going back until 1991 and here are mp3 files for the listening section.
It's not all good news, however, as I've noticed some of the listening files are virtually incomprehensible, presumably because someone simply snuck a microphone into the exam center.
At least for the other two sections I now have a lot more to practice on, and in my first attempt at 1991 I managed to answer a little over 60% of the non-listening questions correctly - I don't know if this translates into 60% of the marks as I wasn't sure of the marks breakdown - but with a pass mark of 60% things are looking promising. I've pretty much nailed the Kanji recognition and production but my grammar could use a lot of work, particularly verb and adjective conjugations.
Right now the thing I'm terrified of is the listening section. This is worth 25% of the total marks and I'm completely awful at it. My strategy for the coming days is to transcribe 2002's listening section as an exercise and compare it to Peter van der Woude's at the JLPT Study Page. Ideally what I need is transcripts of the listening sections for all of the past papers I've now downloaded but these seem impossible to get hold of.
I do still have the book of 2004 - 2006 exam questions and answers which does include the listening transcripts and, hopefully, high quality listening audio but I'm still aiming to hold these back until Sunday, with a week to go, and treat them as proper exam rehersals.