I've not much to add other than, if you look hard, there are out-of-the-way places like Yaringa Marina, Westernport, that, being private rather than public marinas, might (no guarantees) turn a blind eye to liveaboards who mind their own p's & q's and stay under the radar. Further afield, around Metung/Paynesville there are narrow creeks and private berths where one could spend a considerable time aboard without anyone being overtly worried.. but a capital city? Nope. Doesn't happen.
The nearest alternative would be a boat-sized apartment at Yarra's Edge with the boat parked in the marina down below - for ~$10k/year plus costs..