Nice one BEagle; and we won't even mention the Philosophy Depaaartment of the University of Woolloomoloo. Do you mind if I call you Bruce??
All good advice above but Bankstown ain't what it used to be. Basair (Darrin Ward) was good, although I suspect it is now very focused on the commercial airline students. The airfield itself is, I believe, a shadow of its former, three parallel runway self, due to the usual commercial and residential pressures and developments. Sadly none of my remaining contacts fly from there, so I cannot give much current useful advice or contacts. I am not sure about converting half way through your licence, but you will certainly have to do their Air Law exam. Be prepared though, they have some very strange (to me, anyway) regulations, and some varying beliefs. Some of the stories I heard about use of carb (carby to them) heat were very strange.
If you're in Sydney, Bankstown would be a good place to start looking but don't ignore Camden. It's a bit further from the city but a bit less regulated and busy, easier access and circuit procedures. Friends have recommended Curtis Aviation and Gostner.
Good luck with the move and with the flying.