[MrPbody]

When you say "brand new 350", do you mean a "crate motor", a quality rebuild, or a reman? I must ask that because many people erroneously refer to a rebuild or reman as "brand new".
That being said, where is your timing set? If you don't know, you NEED to. How recently has your exhaust system been serviced or checked for restrictions or collapse? An exhaust restriction can certainly cause the symptoms you describe. Catalyst? If it's a catalyst car ('75-up), running extra-rich can clog the converter.
Those Edelbrock carbs have been a real sore spot for many. Most pro builders will refer you elsewhere. If yu want a Carter carb, buy a real Carter. Q-Jet and Holley are far superior. (IMO, based on experience, not advertisement)
Lastly, if all these things check out well, pull the valve cover on driver's side and check cam timing with a degree wheel.