I am in the ACT so can’t advice on the peculiarities of NSW law but it seems really odd to me that the OC can’t simply resolve to use common property as it wants to. The BBQ isn’t for your exclusive use; it’s for the whole OC and you just happen to be lending yours to the OC to use where it would like to have a BBQ.
I still don’t see why the strata manager is bothering to create work for themselves. If the owners are happy, why worry beyond advising that they might want to formalise things.
Also, there are only 12 of you. Why do you need to pay the strata manager to have a meeting? A meeting can be called and held without them. You could do it in one of your units or with camping chairs in the carpark. Just comply with whatever notice requirement are set out in the NSW Act. The secretary can produce minutes. The chair can chair etc.