An own-admission authority school such as this one can appoint its own appeal panel, use a diocesan panel (i.e. an appeal panel appointed by the diocese to handle all appeals for catholic schools in the area), or buy in the services of an LA panel.
You do have a case. Whether it will be strong enough to outweigh any prejudice to the school, we cannot say. You have to keep in mind that on average around two-thirds of appeals do not succeed, the success rate for foundation schools tends to be lower than average, and the success rate for voluntary aided schools tends to be even worse.
13. Chances of success at an oversubscription appeal viewtopic.php?f=35&t=15025
In terms of structure, set out your written statement on one side of A4, with a separate section on each of your main points (such as Christian commitment, music).
If there are any minor points, make clear that they are minor points and don't overdo them.
Attach as much evidence as possible (e.g. "Appendix 1 - baptismal certificate", "Appendix 2 - letter of support from Anglican priest", etc.)
Worth making clear your respect for catholic education.