Simple: Write a letter (slow mail type) to each tennant and tell them that because the mall will not allow your legal carry you will no longer shop in their store. Enough people do that and the tennants will force the mall to change it's policies.
BTW: Private property that is open to the general public is not "private"...it is very regulated...and all this can change by legislation too. You don't think so? Then why then, after the Americans with Disabilities Act was passed did all of the malls get self opening doors? and level entrances to accommodate the disabled?