I would say keep adding the zinc at each oil change but at a lesser amount, like 4-6 ounces with each oil change just as a preventative as modern oils have removed the zinc that used to be there all the time. Cam break-in is the most critical time but it still needs to be there all the time.
If you are going to run solid lifters in a BBC know that the heavy valvetrain and staggered lifter layout makes these engines real hard on cam lobes. I would consider it MANDATORY that you use a face-oiling lifter, these have a tiny oil hole lasered right thru the center of the lifter face to constantly oil the lobe. I wouldn't even bother picking up a wrench without them.
The 2399F60 is an open chamber piston, you will likely have to rework the head chamber or the piston dome to make them fit with your closed chamber heads. The 2349F60 piston is the correct piston for the closed chamber head but but is higher compression out-of-the-box than you want, you will have to just mill the domes down a little to get the compression down to 10-1. This would be easier to do than hand clearancing the open chamber pistons IMO