I’ve built and run in a few engines and here’s what I’ve always done.
Upon starting up the engine, I break the cam in (not needed for roller cams) by running it for 20 minutes modulating from 2,000 RPM to 2,500 RPM. After that, I change the oil. Then I drive the car 100 miles, trying to vary the engine speed, but not hot rod it. Change the oil again. Then go up to 1,000 miles doing the same thing. Change the oil. After that, I go with normal engine oil change intervals.
As for oil, I typically run a straight conventional oil during the break in period as well as a zinc additive to protect the cam. I like to use Lucas Oil’s zinc additive in my car. After the break in period, it should be safe to switch to synthetic, but you still need to use the zinc additive or an oil with it added in if you are not running a roller cam.
So that’s the generally accepted break in procedure. At 300 miles, your rings should be mostly seated by now, but it sounds like you have a lot of blow by. At this point, I’d highly recommend you get in touch with the engine builder and trouble shoot with them. It is better to bring a problem to their attention now than after you’ve driven it a lot. If there is something wrong, you have a lot more leverage to ask them to make it right if there truly is a problem.