My 340 in my 66 developed issues :-(

I was told that the exhaust manifolds I have flow better then headers. Is there any truth to that? a nice set of headers for that car cost over $700.00 and will require a mini-starter, I'm thinking I have to fix my exhaust problem and that may be attributing to the intake getting hot/baking my carb.. What do you guys think? Headers or my manifolds?