what oil to use

I can't think of any pro race series where they use a flat tappet cam, it's all rollers which the zinc or lack there of is a non-issue.

Nothing wrong with using race oil as long as you are changing real often since they don't typically have the same level of detergents and other additives needed for the oil to last in a street car application.

Also, if you are getting your "race" oil at a local part store chain it likely has an API service rating like Valvoline VR1 which comes in "off road" and API version. I have never seen VR1 on the shelf of a parts store that didn't have the API SM rating which means it doesn't have any more zinc than any other SM rated oil.