Oh boy. Everyone has an opinion on engine oil! I'll give you mine.
Never synthetic in these engines. The clutch/seals/gaskets weren't designed for it. The oil should be changed every 3k miles (plus or minus), so the long lasting benefit of synthetic oil is moot on these bikes.
As far as zinc, I do have some experience with that too. I've rebuilt a bunch of cb750 engines now and, after talking with a lot of people who have built far more vintage engines than me, I am convinced that breaking the engine in with an oil that has zinc is probably a good idea. It adds a layer of lubrication as the engine "seats itself" into healthy operation. BUT, oil with added zinc can be corrosive if left in the engine too long.
So, I use it for the first 600 miles of breaking in an engine. I never stay at the same RPM for more than a few seconds and I slowly work myself up to higher rpms as I get past 300 miles. At 600 miles, I drain the oil and use Honda GN4 oil.
Its worked for me!