Even though the lenders are no longer able to talk to the appraisers (according to recent rule changes), the real estate agents still are. Perhaps the listing agent could talk to the 2nd appraiser and see if the appraiser had accurate facts about the home or its competition. Now, listing agents must be prepared to "sell" the appraiser, just like a buyer. We agents need to see our competition, so we can tell the appraiser about the defects in them that make our listing either not a good comp to them or worth more. We need to know the facts of the neighborhood, what makes our listing worth the price we have asked.
Failing that, perhaps a third appraisal is in order?