Dear Suet suet~
I'm sorry things are not working out at the moment. As you know the higher Medicare rebate reflects the extra training a clinical psychologist needs to qualify.
From one perspective it is not so much the qualifications on paper that are significant as the interaction between the therapist and yourself. You've mentioned the current person is not a good fit, and that you have an engagement problem, and do not have a workable regime which you can apply outside of sessions. Plus you do feel the need to lean on your therapist, and I guess at the moment are not able to do so.
All that being said I wonder what value there is in continuing as you are? The number of Medicare rebates available in a calendar year is strictly limited and really need to be spent on the best help available.
At the moment you seem to have two related problems, first to find a GP, and second to find the appropriate therapist. Not easy, sometimes word of mouth can be of help. Have you heard of a GP that might be suitable as a starting point?
In my own case I've had a lot of interaction with psychiatrists, who generally have been very helpful. True they are more expensive, however there is an annual softy-net cap which does limit this. They have on occasion referred me to clinical psychologists for specific therapies, from which I've had mixed results.
Would you consider a psychiatrist as an option?