People don't do appraisals generally because they don't care about them. I would simply ask the president if he or she cares about the appraisals so you know whether or not to waste any of your time on trying to collect them. If he or she cares about the appraisals, tell him or her that you need some power or some backing in order to extract them from senior management.
You might suggest to top brass that getting appraisals in to HR on a timely basis be one of the things managers are appraised on.