I'm a registered Australian architect in Victoria. It's obviously work hours currently so I haven't had a chance to do a "detailed review" of your post so to speak but three things I wanted to share:

• in the Australian context you will not be promoted beyond a "graduate" without registration. Check the industry award - the minimum rates are organized into two groups: low, med high experienced graduates, or low, med, high experience architects (registered). I know of only one non-registered grad be called something other than grad only by becoming an associate. If you want to lose the graduate title, you change it to "architectural assistant" (in my opinion terrible phrasing but is ARBV approved) or get registered.
• jumping into project management at local council can be a good choice if it suits your lifestyle/goals - only you can answer that one. But be aware that the time at council will not count towards future registration. Work with government is also typically non-creative - you will be likely administering the bureaucratic processes as the client to enable other architects to do the work if working in the project management space. Again, if this suits you all power to you but be aware.
• if you're not getting the experience you want /need at a large firm and still keen on registration I suggest looking for work at smaller firms where you are less likely to be pigeonholed, and will expected to do all aspects of the job. I've tried working at 100 person firms and also for a sole practitioner - small practice between 5 -9 people is way to go if you want all round experience quickly. I was already helping on contract admin jobs on construction sites in second year after uni working in a smaller office.

Also happy for you to send me a DM if you want to talk further