I’d say you are pretty much stuffed.
The only argument I can see is for discrimination against you by not applying the bylaws universally.
Take photos of the cats roaming common areas and other dogs not being carried over the common areas to show the bylaws aren’t being applied fairly. You could even take photos of resident cars parked in visitor parking bays, rubbish left on common areas, etc to show the EC aren’t applying any of the bylaws consistently.
If you took this to conciliation and then adjudication I believe you would loose BUT the adjudicator might insist that the EC enforce the bylaws against the other pet owners not complying with said bylaws.
Informing these pet owners of your intention (and one of the consequences) MIGHT be enough to cause the EC to reconsider action against you.
I believe OC should be allowed to restrict pets but only if they apply them fairly to everyone.
Haven’t found a def of Strata Visitor for NSW and the one for QLD was from an article commenting on the ruling but I’ve been unable to find the ruling.