You sound so miserable :(.
I think its a balancing act. "Term" is generally considered 37 to 42 weeks, but there was some research out a couple of months back that during the 3 weeks from 37 to 40 weeks babies do still develop quite significantly in utero - IIRC a substantial amount of that was to do with brain growth. If they're planning an elective CS for something like a breech presentation then it will normally be scheduled for 39 weeks. Not all women/babies will go to 40 weeks, but I think the consensus is there's a big difference between a spontaneous labour at 37 weeks and an induction.
In addition, if you try and induce before the mother's body/baby are ready it is a lot more likely to lead to a long, hard birth. Once you've started induction there isn't really a way out until the baby's born.
That said, if the mother is in pain and/or has health issues that are being directly impacted by pregnancy then that should be taken into consideration and a compromise should be found that aims to relieve the mother's distress with minimum impact to the baby. Whilst the ideal would be to wait and labour spontaneously, most babies born after 37 weeks will do absolutely fine.
Do you have any supportive Health Care Providers sympathetic to your situation? Have you talked to your GP? I think you need to try and find a consultant who is likely to sympathetic and will actually make you feel as though you are being listened to and taken seriously. They may still not recommend induction as early as you would like, but at least you should understand why they want to hold on and what might change that advice.
If your GP isn't helpful you could also ask to talk to the Head of Midwifery or a Supervisor of Midwives - they should be interested in making the women cared for by their team feel supported and they have the authority to fight your corner for you. You might also want to talk to AIMS, who should be able to advise on how to get more support (although how much energy you've got for letter writing and being bolshy belligerent assertive at this stage I don't know.
Whatever happens (and whenever), I hope the birth itself is straightforward and your symptoms ease quickly after your baby's out :)
(ps - if you do decide to try for a natural induction, please please please don't take castor oil. Its far more likely to make you feel really ill than it is to bring on labour - and if you do happen to go into labour while recovering you'll have a really miserable time.)