assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/275897/school_admission_appeals_code_1_february_2012.pdf
Section 2: Appeal Hearings
Timetable
2.1 Admission authorities must set a timetable for organising and hearing appeals that:
a) includes a deadline for lodging appeals which allows appellants at least 20 school days from the date of notification that their application was unsuccessful to prepare and lodge their written appeal;
b) ensures that appellants receive at least 10 school days’ notice of their appeal hearing;
c) includes reasonable deadlines for appellants to submit additional evidence, for admission authorities to submit their evidence, and for the clerk to send appeal papers to the panel and parties;
d) ensures that decision letters are sent within five school days of the hearing wherever possible.
OP, to have operated within the law, no admission authority in England, be it own admission authority school or local authority, can have held a 2019 main admissions round appeal last month. 29th March was the earliest date that could have been set as a deadline for submission of an appeal by the parent, being 20 school days from national offer day (i.e. 4 school weeks, with no intervening holidays / bank holidays).
Your big mistake was only namimg one school on your CAF, when your main issue was the desire not to be allocated a place at one specofic other school. If you had heeded the advice published by your LA on how to complete your CAF, it should have been possible to have named at least one other school amongst your preferences where your DS could have been offered a place om March 1st.
In submitting an appeal against your DS being offered a place at a school to which you have now made a late application, you are appealing for a place at that school, not against the school you have been allocated, so if you really have submitted appeals for 14 schools, you have to present 14 specific cases. However, 'if you are able to provide appeal panels with documentary evidence of the danger that your DS faces in attending his allocated school, you may find that this helps to influence (at least a majority of) the members of the panel hearing cases for one of the 14 that the disavantage to your DS of not going to that specific school outweighs the prejudice to the efficient use of resources of that school having to accept an extra pupil.