I'm sorry but you are dreaming, if you expect to find any labs doing E6 in Melbourne (or anywhere else in Australia, for that matter) that aren't "pro". There is a chap in Melbourne who runs his own replenished E6 line but from all I have seen and read he takes a quite professional approach to his chemistry and processing... The days of chemists, supermarkets, or other retail outlets providing or, even, arranging, E6 processing, have long since gone. As suggested, Vanbar provide E6 processing in Melbourne.
Regarding C-41, for 35mm you could try your local BigW. Our local until recently offered $5 C-41 per roll process only. I think they may be in the process of centralising this, however some stores still process in house. Quality depends on who runs it. My nearest was excellent until it stopped a few weeks ago.
There are likely to be a few camera/photo outlets in Melbourne that still provide in house C41 as well and probably 120. We have two in Hobart and another in the suburbs. There must still be a handful left in a city the size of Melbourne.
Australia is a wonderful place to live, indeed, however if you ventured here looking for cheap film and or processing, I am afraid you have come to the wrong continent.
Regards
Brett