Factory rocker defeated by pushrod.

Thats a common issue with stock rockers, especially when you up the cam. I have seen 318 2 bbls do it too.
The replacement rockers from mopar performance were beefier in the pushrod cup but I dont think they sell them anymore.
I dont know if stock 340's were thicker but they did have a different shape to clear larger valve springs.
Btw, not all 273 rockers were adjustable. They switched to the stamped rockers around 68 or 69 if I recall.