Have you inspected the rocker arm tips where they contact the valve stems? They should be smooth, without any cupping or scoring. Rocker arms can be refaced, using a fixture on a valve grinding machine that sets a specific radius and smooths out any wear or cupping from running with incorrect adjustment. There's no reason for a 216 with correctly adjusted valve clearance and a camshaft that's in good condition to be any more noisy than any other engine with mechanical lifters.
In about 3- - -2- - - -1 seconds, one of our resident engine building gurus will sound off with the comment "It's impossible to get the proper radius on a reground rocker arm!" Ignore that advice. Uniformity between rockers is far more important than some imaginary ideal radius.
Jerry