Perhaps some sort of wierd adjusting may be required, since isn't the 1405 a manual choke originally? I'm not sure about that part. Read the manual, it's downloadable from Edelbrock. It SHOULD only have to be turned rich enough so the choke plate is closed when dead cold. Turning it richer will force more pressure on the bi-metal coil so it takes longer for for the electricity to 'unspring' (that a word?) the coil/choke plate open. If you're having hard start problems, and turning the choke plate richer isn't helping, you may have a bad choke cover/coil. Could be something else entirely.
Also, you're describing two different things. Hard starts. Hesitation when driving, yet running great when fully warmed. Is the hesitation only when driving before fully warmed up? If so, the choke COULD have something to do with the hesitation before fully warm, if the choke plate isn't open all the way (because it's not to operating temp) then you're bogging the engine down with extra fuel with the choke plate still partly closed, getting an incorrect A/F mixture. Althrough with linkage, it should make the choke plate open all the way when driving. Which sounds strange I know, because that is what the choke does, but not for driving, engine under load. Like I said, could be something else entirely.
What carb did you have before? A stock Q-jet with everything attached? There's a lot of things that go with cold starting just in the carb/emisisons/drivability alone. Stock, you have heat risers to warm incomming air, Computer controlled carb, double pumper carb? A lot of that stuff that is usually tossed with a 80s smog motor has a lot to do with starting and warming up your motor. Where as an older pre-smog era engine set up, has the same stuff, but it's all manual, heat risers, exhaust passages in your intake to warm the carburetor, choke with vacuum breaks. IMO, slapping on a Edelbrock usually gives you a lot of problems. Hard starts being one of them.
I think I just confused myself.
I'd say, get your choke/warm up/hard start condition figured out first, then see where your hesitation problem lies. Fixed, or still unresolved, go from there.