Before adding any more bypass air remove a small manifold vacuum hose and see if it helps.
More times than not there simply isn't enough idle fuel available to the mixture screws.
Not saying here that you may not need more bypass air, but it will only make things worse if you don't have enough idle fuel right to start with.
More specifics would also help:
What is the carburetor part number and exactly what has been done to it?
The details from the cam card would also help.
A 240 @ .050" flat solid cam really isn't that big, but if it's ground on a 108 LSA it will have enough overlap that idle quality will be degraded considerably in a the 396 engine........Cliff