Hi.
We moved over with the lateral transfer system in 2007. From first applying to arriving in Australia it took us about 10 months. We did the same as you and put in an expression of interest. We then went for an interview in London, all the family went. On the day they give you a yes or a no and from then on, the process of applying for a visa was started. We did all this ourselves, including medicals, but we did get reimbursed by the ADF when we arrived.
There seemed to be not too many laterals coming over in the past few year, but that seems to have changed. We are posted to Darwin at the moment and there seem to be quite a few coming over. As regards keeping your rank, most people have to drop a rank or two when they come over. My husband dropped from a WO2 to a SGT.
Please bear in mind that this was 8 years ago and the process etc may have changed. You can always send me a message if you need to know anything else.