I have a 428 in my '68 bird. The motor is still running it's break in oil and it is time to change it up. It will be the second oil change since the rebuild.

Do you think it would be okay to run something like the amsoil 10w40 (high zdpp) now? Or should I go with something else?

I personally would go with Valvoline Racing oil, its has ZDDP in it. Alternatively you can use a regular Valvoline 10-30 with 1 quart of Marvel oil... http://www.jegs.com/i/Valvoline-Racing/949/VV205/10002/-1

Here's my oil philosophy for what it's worth. Use regular high quality oil such as Valvoline and add Camshield or other source of ZDDP. Regular oil has the right amount of detergent. Racing oils have less or no detergent and diesel oils (Rotella, etc) have too much detergent. My philosophy is just based on what I've read and heard over the years that makes sense. I'm no expert.

X2 for Valvoline Racing oil. It's what my builder uses (professional racing engines) and told me to use.

Don't drive when cold here, so slightly modified gets 30w Valvoline.
Street/strip car(6500 rpm) gets Valvoline Racing.

X3 for Valvoline VR1.

Brad penn

I'm no expert either, but since you asked.
Break in oil is just that, break in oil, not oil to use for the rest of your car's operational time span.
To properly seal the rings and condition the camshaft, additives are required that normal everyday oil does not have. Years ago most oil had all the additives needed but not so now. Without proper additives, ie zinc, your camshaft could be toast shortly after you start up the newly rebuilt engine. Once the engine is "broken in" you can switch to normal oil.
I used Joe Gibbs break-in oil in my 428 then switched to Castrol GTX.
There are millions of cars and trucks operating just fine without any adverse effects from using ordinary off the shelf oil. Now if I was running my car in the Indianapolis 500, I would spend the money on racing oil.
I've owned my 1951 Panhead since 1979, my F250 since 1986, my SBC powered boat since 1990 and my Firebird since 2007. I use ordinary oil in all and they operate as they should.
Just my opinion.