A parish meeting is a meeting of the parish, and should allow electors of the parish to raise and discuss whatever matters they think appropriate. Although the council chairman must chair the meeting if present (and likewise vice chairman), as you say, anyone can be appointed chairman as the first item of business.
One thing to watch out for is that the parish meeting may have standing orders, and these can be decided by the parish council. However, they must not be unduly restrictive, and should be only such as to allow an orderly meeting.
As you say, parish councillors have no particular status at a parish meeting, so it is the electors whose meeting it is.