I was facing this decision a few years back, although DD had been breech from 28 weeks.
In addition to AIMS (and specifically their publication "Breech Birth: What are my options" by Jane Evans), I found "Breech Birth" by Benna Waites and googling Mary Cronk to be very useful and informative.
We did a lot of reading and talking and thinking, and ultimately did go for a planned HB of a breech baby. Fundamental to that decision was knowing that our IMs had, between them, substantial breech experience (far more than I was likely to get in hospital) and that we would be aiming for a very unmedicalised version of breech birth. I had talked to the hospital about vaginal breech and I'd have had a CS in preference to the birth they described (this article by Mary Cronk summarises the differences).
littlebrighteyes - as its your 4th you may well find the hospital are a lot more open to the idea of vaginal breech. They'll like the fact you've had 3 births already and so have "proven" your pelvis (hate that expression, but might come in handy). If its a route you want to pursue its worth asking for an appointment with a Consultant Midwife or Supervisor of Midwives, either of whom should be able to advise on the breech skills within their unit.
LearningFast - have you pushed your IM on her breech experience? My guess would be that she doesn't want to lead you into a decision that is against NICE guidlines, but would support your wholeheartedly if you made that decision by yourself.
Something else that has some good reports is a chiropractic method called the Webster Technique - it assumes there is some tension in the muscles that support the pelvis, which is causing a torsion in the uterus that is constricting things such that the baby can't turn. By releasing the pelvis you, hopefully, remove the muscle problems and free up more turning room. If you decide to try it, make sure practitioner has suitable training (as with all these things). Knowing the logic I suspect any physical therapist (physio, chiro, osteo) has the potential to help if this is the problem.
Deciding how to bring your breech baby into the world is a horrible decision and I firmly believe there is no universal right answer. We did a lot of talking, reading, thinking and soul-searching before coming to our decision. It wasn't one we took lightly at all and neither will it be the right answer for all other women carrying breech. All any of us can do is to make the most right (or least wrong) decision we can, taking into consideration our situation and support at the time.