New engine no oil

[Speedster 229]

I made one of the largest mistakes ever!!!!! And I need some advice. But first the story.
I primed the oil pump started my new 350 crate engine , broke in the cam for about 30 minutes, drained the oil, installed a new filter and started the engine again. Thats right ,no oil!!!!!!!!!!!!!!!!!!!!!!!! I was running open headers so i didn't hear anything and it didn't get hot. Ran it for about 3 minutes and when I let it down on idle it quit. Starterhad a real problem turning it over. After trying about two times , what I had done hit me like a ton of bricks!!!!!!
I drained the oil. New filter and this time 4 quarts of new 10/40 valvaline and I put in one quart of Lucas oil additive.Primed the oil pump and started it.It started hard but ran well. No valve noise or other bad noises. I now have mufflers on it and have it tuned and running well.
It smokes pretty bad when it first starts. Can't tell if it uses oil yet as I haven't driven it yet.I'm still assembling the truck.What do you think?? Should I stop now and have It rebuilt? Do you think I ruined the rings? Will they seat ? Could I have ruined the valve guides??
Because it runs well, I'm just concerned with the smoke. If you think it will cure itself I'd like to continue assembling the truck but if I should pull the engine, now would be the time before final paint etc.

What would you do?????????????????