ILR inkstamp renewal in new passport

My Australian passport expired (I finally got an interview in to renew on 16th), however I've read somewhere from law resources that this means that I cannot ratify my right to work with my expired ILR inkstamp (2010-2020).

I never received a BRP or BRC because I received my settled status before that was compulsarily introduced.

The application to get a BRP mentions providing current right to live in the UK. Will my expired passport with my old inkstamp do? (in addition to proof of living such as banking and drivers' docs), I don't really understand what else I'm supposed to provide since I missed out on getting a BRP through a quirk of timing.

Alternatively is there a way I can get a new inkstamp transfered over? I'm looking for preferably the cheapest, quickest way to regain proof of settlement on paper since I intend to be applying for jobs in a new field soon.

You only have the option of applying for a BRP. There is not other option.

Why not apply for British Citizenship?

Please note that since Immigration Act 2014 came into force, you need a valid BRP to officially prove your immigration status for employment and use of public services. This means you need it for any new employment, to rent a place, to open a bank account, to use the NHS or get a driving license. No sticker or paper is issued for settled status