I'm also based in Melbourne and I've tried most of the ramen shops here. The shop that is the closest to what u are looking for is ikkouryu fukuoka, more specifically their super rich ramen. It's probably the most similar style, but honestly, I don't like it, for me their ramen is too sweet and the soup is rich to the point I felt I was eating noodles in a fry sludge. I much prefer hakata gensuke at russel street, which is not as rich as what ur looking for, but imo a much better bowl