My comments must be qualified by saying that I am not a professional adviser, but only giving a view to the best of my knowledge. The procedure followed does not seem to be valid because the right to exclude the public cannot be exercised selectively, and must be done by means of a specific resolution that gives a reason for the exclusion.
There is a possible loophole that would need you to check the council's standing orders. Voting must be by show of hands unless the standing orders provide otherwise. If the standing orders allow the council to opt for a secret ballot, then the council could have avoided making public how the votes were cast.
The problem with pursuing the matter very far is that it is quite possible that any adjudication might say that the procedure followed was incorrect but that there is no evidence that it affected the decision.
In general, it is quite difficult for local councils to make decisions that they know will be badly received by applicants who are necessarily local. In an ideal world, councillors decide the matter in an impartial way and applicants accept the decision with good grace. But things don't always work so well, so from a distance, I have some sympathy with both sides!
A separate point for you to keep in mind is that the parish council is only making a recommendation, and its recommendation will only be taken account of to the extent that it raises matters that involve valid planning considerations. Mere opinion is not relevant. The planning authority has to make a decision based strictly on the planning considerations, and can only take into account the parish council's view to the extent that it is relevant. And even then, the planning authority can (and regularly does) decide against the parish council. Your main aim has to be to persuade the planning authority of the virtues of your application, using relevant planning arguments.