You can agree to do GPOC at any time as long as you meet criteria, you don’t have to wait until the meeting after elections. So if you do it in year 2 it remains in force until the elections in year 4.
However I feel you are being a bit unfair to the Clerk as even if they did pass now, with 8 out of 15 Cllrs co-opted you don’t meet that criteria
As to the staffing agenda, yes it should be published as normal, with only the apologies, and minutes open to the public, then the meeting closed to public. It’s perfectly acceptable in my view to have something like staff matters as a agenda point, that’s what goes on our agenda and minutes should be published but are very likely just to say it was resolve to agree to the Clerks request or some such as staff employment matters are not open to the public