I don't think it is running out of fuel. If it was bad enough that it won't pull in first then it would be completely gasping in second and never make Drive.
Did they cut the heads when they rebuilt it? If so, how much? Adjustable rockers? If it still has stock rockers and the heads are cut a bunch it could be pumping up the lifters and floating the valves slightly. While we are on the subject of valve train, was the cam degreed?
What does it have for compression pressure?
Also I would pull the pan and see how far off the bottom of the pan the pickup is. They don't rattle for no reason.
