I do not especially recommend adopting an amendment of the bylaws to accomplish what is desired. The better way, I think, would be for the general membership assembly to adopt a special rule of order, applicable only to the executive board. The vote required to adopt a special rule of order is a vote of the entire membership or a two-thirds vote only if previous notice has been given.
I agree with Mr. Honemann that it is unlikely that the bylaws of the organization mention the board having the authority to adopt its own, permanent special rules of order. Not only would the adoption of such a rule by the executive board be null and void, it would also be an act of usurpation of powers rightfully belonging exclusively to its superior (i.e., insubordination), for which appropriate punishment can be inflicted upon those who are guilty of the act.