Sounds like a fuel delivery issue as Masterbeatty stated. Check the fuel pump as well, is it mechanical or electric? Pickup a cheap low pressure gauge and check the fuel pressure, if that comes back good then check the flow. Flow should be about 7-10 gph for a mostly stock 400, heavily modded could require MUCH more. How to check flow http://www.73-87.com/7387garage/drivetrain/fuelpump.htm
Another thing that comes to mind since you swapped heads and a cam. What CFM rating are the carbs you've tried? You might be running out of Cfm at the carb with the improved heads. What are the specs on the heads? Is the RPM verified with a Tach or just an educated guess?