What adverse consequences can I point out to persuade my HOA to cure a violation of the rules/regulations/bylaws they are responsible for enforcing?

I strongly urge you to hire counsel to pursue this.  I think the first step is to provide written notification to the Board, and you probably will need to cite statutes and applicable provisions of the association documents.  That is why you need a knowledgable attorney.  Also, since you mention an upstairs unit, I assume you are dealing with a condominium association and not a Homeowners Association as you indicate.  This can involve a higher level of fiduciary duty on the part of the board, and I think it is in appropriate for the property manager to give you the response that he or she gave.  Ultimately, it may be necessary to file a complaint with the Florida state regulatory division for condominiums, and maybe also against the property manager if they have given you advice that is wrong.  It is primarily up to the Board to enforce the regulations of a condominium, but if they do not, you may need to also file a private enforcement action.  An experienced condominium attorney can advise you about that. This is specific to Florida law and does not constitute legal advice as the facts presented are anonymous and incomplete. This is intended for general education only and does not create an attorney-client relationship. This should not be relied on and you must seek your own attorney client relationship.