I did not know the committee votes applied to positions other than those recently vacated by outgoing senators until just now. I will abstain from voting, because I've been largely ignoring whatever talks have been going on leading up to this point and lost my NS seat before even realizing it was being contested.
Both the NS and Judiciary had requirements that they be "selected at the beginning of the Senate". Only the GOR lacked that clause.
Since the GOR committee's enabling resolution lacked such a requirement, I believe its members would continue to serve for as long as they're in the Senate- Article 7, Section 3, Clause 3, describes how Senators are elected to a committee once it's established, but it only describes the election of new Senators in the context of a member of the committee resigning from office.
However, a potential workaround here is a selective interpretation of 7.1.3 ("The Senate as whole shall elect it's members to each committee."); if we define "The Senate" in that clause as referring to that specific session of the Senate, rather than just the Senate in general, then GOR Committee elections are definitely still legit here even without any explicit requirement for them.