There really isn't any Dojos that I know of that are full time, most are 4-5 days in the evenings (some have weekend classes).
There are a few choices that fit your criteria to varying degrees (and in no particular order):
Joe Thambu - Yoshinkan Aikido (http://www.aikidoshudokan.com/
) - bloody good from all reports although I haven't seen him teach yet (will soon, seminar coming up :P ), not sure how big his joint is.
Michael Giannone - Iwama Aikido (http://www.riaiaiki.com.au/
) - My dojo of choice, Michael is an excellent teacher, but is only a Nidan (under Mic Marelli Sensei from sydney). The dojo is only a few years old, and relatively junior, but the atmosphere is very friendly and open.
Sonny Rehe - Iwama Aikido... Dojo is in fitzroy, kind of small and cramped, but has a generally more experienced level of deshi. Not sure what his contact details are unfortunately. I've been to a seminar or two with guys from here (one was at the dojo) and they're a tops bunch, not sure how open the atmosphere is during classes though (I haven't seen any), but I can't imagine it being anything other than constructive.
There are some others around like Barry Knight et. al. but I haven't seen any of their classes or heard much about them so I can't comment...
There really aren't many large dojos in melbourne, it's just too hard to pay the rent to have a small class in a large space... The biggest is Field Aikido (http://www.martial.com.au
) but it won't meet your requirement for no elitism within the school, it's heavily 'ranked' and has a more closed atmosphere than most.
I have heard of your old dojo and it's definitely an exception, in part probably because of the way, way lower land values in Perth, inner city melbourne is a nightmare for rent so almost all dojos will be pushed for space.