When you did the valve lash, did you notice any scratches or uneven wear on the rocker arms? Did you also check the cams for any scratches or uneven wear?

I have never had a problem with more noise after a valve lash adjustment, so there may be a problem with worn out rocker arms or cams.

I don't know if a B16a has lost motion assemblies like the B18C does, but if it does, check those too. Just press down on the plunger and if it doesn't move smoothly, it could be a source of the problem and it needs to be replaced.