I did exactly what you described and got the job part-time!! I wrote a covering letter saying something along the lines of 'happy in current job, but looking for something closer to home (had a 60 mile round trip) and roughly 0.6. Understand job is advertised full time, but if they would consider part-time I would love to work for them'. Sent 2 applications at roughly the same time, both to high achieving grammer schools. Got an interview at one, and got the job over 3 other candidates. As school budgets are being cut, it might actually fit the school better. I think jobs are rarely advertised as being part-time as most people want full time. You have nothing to lose. You are happy in your current full time position, so are not putting that at risk. You only want to move if you can find a part-time job so you're not limiting your chances of getting a full-time job. An honest, upfront and enthusiastic cover letter, along with a thick skin, should do the trick!