I sorted my medical last week - as it was due to expire in August anyway (initial was in 2012) and it's one less thing to worry about. We will need to arrange financing when the time comes of course...
I was also asked by BA about how soon I could start, and then asked the same by CTC via email - in both cases I advised of my current three-month notice period, and this has been respected.
I am aware of only two start dates for OAA at present, 7th September and 9th November, but would welcome hearing from anyone who knows of further dates.
Thanks to Geoff565 and 4015 for the corrections on my earlier post - I've edited this to reflect the updated info.