This is all a bit complicated, not least by the fact that you don’t want the cage any more.
There is another issue, which is that owners often think they have the right to build the cage to the edge of their parking space, which is not strictly true. Parking spaces are designed with the assumption that the residents’ car doors can be opened over the adjoining spaces. A cage on the boundary of the parking space doesn’t allow for that (not that I’m saying this is the case in your situation).
Then there’s the question of what’s allowed to be stored in the cage, and the visual impact of the cage, all of which leads many strata schemes to use their common property rights to ban storage cages altogether.
Given the non-communicative chair, I would now conduct all your communications in writing. Actually, this would be my advice in any circumstances. Verbal agreements aren’t worth the paper they’r not printed on.
And given that you no longer require the cage, I would suggest you go on to AI (Chat-GPT or Claude.ai) and ask it to write a by-law compliant with NSW strata laws, that would allow you to keep the cage. BTW, if you wanted to keep the cage, my advice would be to consult a lawyer about the by-law.
Then send the by-law to the secretary of the scheme and ask for it’s approval at the next General Meeting. They will probably reject it, you can apply for mediation at NCAT, they will still say no but by then the war in Iran will be over, the Straits of Hormuz will be open, petrol prices will have returned to normal and there will be a whole new flock of lambs that require protection.