340 Cold Valve Lash Unknown Cam

Another thing to consider:
You say you have "273 adjustable rocker arms". Are they stock, or have they been adapted to locking adjusters? The stock friction fit adjusters get notoriously loose after 60+ years of use and may not be holding the proper adjustment, leading to the noisy valvetrain.
MRE Shaft-Type Rocker Arm Adjusting Screws
Converting involves spot facing the arms so the locknuts have a flat surface to seat against. You may also want to check the rockers for spring/retainer clearance, since they can interfere with some aftermarket springs. It can all contribute to excessive noise.
But when all is said and done, don't expect it to be as quiet as a hydraulic tappet motor- there will be a bit more with solids. Kinda depends on what your definition of "noisy" is.