Edelbrock head valve spring assembly

Getting back to the OPs question
this is how I see it;
Those thin shims siting on the aluminum are not strong enough to survive the spring pressure. The thick ones are. And the thin ones were an attempt to prevent the grooved ones from eating the head. Together they work. Either one alone will not. Best solution is the cups.
I just can't see a little extra pressure(less installed height)on a mild lift cam being a problem. I have a mild cam(230*). With the extra pressure, she revs to 7200plus. And since the combo is still pulling up there, I go there a lot.Stock 340 cams were done early back in the day. Mostly because they went into pump-up. They still had life after 5500.
OP, Since you ordered the cups, make 'em fit and sleep well, knowing they will protect your heads while working towards achieving the required installed height.