So what was rebuilt. Is it bored,new rings and bearings but re-used the cam. If so the only break in truly required is to seat the rings. The cam was wear hardened(work hardened) from already running previously.
So truthfully you don't even need the 1000 mile change. Just the 100 and 5000 mile change.
The non syn recommendation is just old school thinking. Today most engines are sent from the factory with synthetic,and many are sent with extremely high moly,so the old school ways of thinking are slowly evolving,and engines are lasting longer than they ever have,so just keep it simple.
Rotella t-5 is a syn blend. If you can find it in a 0w30 or 5w30 those would be my first picks. They ultimately will flow the quickest at start up. The straight conventional 10w30 is proving via used oil analysis to be a great oil at longer than average drains nd shows consistently low wear metals.
Any of the rotella lines will have more than enough zddp for you and your new engine.
Or buy a dedicated break in oil and simplify the entire issue.
Personally the whole recommendation of not using an SM/SN oil is just their way to cover their a$$ and shows their utter lack of evolution and not knowing what the vastly superior oils of today are capable of.
If you can find devlac elite 222 0w30 I would buy it by the 5 gallon pail and use it exclusively in that motor for life. Every 5 gallon pail is enough for 4 oil oil changes and that oil is easily good for 10000 miles.
And being an hdeo tells me zddp levels will be more than enough for the cam.
Today's oils are so complex that simply requiring an oil high in zddp isn't even really saying anything useful. Some oils may have slightly less zddp however they've got such high levels of friction modifiers they don't require the zddp.
So blanket statements really show a level of antiquation and lack of any real understanding when it comes to lubricants,the additive packages and the synergism when a final formulation is ready for use.
Zddp is a dinosaur in the lubrication world.