I had this exact same problem when I installed the MSA larger front sway bar to my 260z. My engine mounts looked fine, but I was told that after 40 years they may droop a bit and this lowers the engine enough to have sway bar hit oil pump. I replaced the engine mounts with brand new ones and all sorted.
So when people say look at your engine mounts, don't bother looking because visually you won't see anything wrong. Replace them and this may solve your problem. Good luck and update us.