As long as you have a majority in favour on Tribunal action, then you can proceed. There aren’t many issues in strata that require unanimous approval, and this isn’t one of them.
In fact, if you don’t proceed, even if other committee members drop out, owners in your block could take the committee to NCAT for failure to fulfill its statutory duties (section 232[2]).
I realise that the “cost” of your time is referring to the effort you are making rather than a financial impost. However, just to clarify, the Tribunal will not compensate committee members for time spent pursuing a case. They will, however, allow for a claim for costs if you employ a lawyer but even then in limited circumstances.