If a person (committee member or any other person) already has a proxy from someone, then they can’t vote your proxy once they reach the limit.
However, it doesn’t have to be a committee member, you can appoint any other owner as a proxy.
If you don’t know any other owner or don’t feel you can trust them I suggest you find a friend who can attend as your proxy, that is the easiest and safest solution.
You have highlighted a gap in the legislation – if a proxy is a directed proxy, i.e. the proxy specifies how the proxy must vote, then it shouldn’t count to the maximum number of proxies a person can hold, because they have to vote that way. (the Corporations Act and ASX Listing Rules have provisions that provide for this, and also re the Chair holding proxies)