Rough Idle Problem- 1967 Valiant

Mine doesn't like the factory lash specs, but runs fine on .013/.023 after being warmed up.
On mine, the valve stems wore ruts in the rocker arms, and I had to make narrow feelers to fit in there so it would lash right. The slanty only fires three cylinders per revolution, so any compression imbalance shows up right away.
Other sources of trouble are;
>Slantys occasionally suck air right at the intake to head juncture.
>There is a gasket between the intake manifold and the exhaust manifold, under the carb, that occasionally leaks.
>the PCV, and/or its hose (which is specific to that duty),
>the Brake booster and/or it's hose, if you have one.
>and any device that is operated by manifold vacuum.
That said;
If your slanty has burned an exhaust valve the piston for that cylinder, at idle, with the throttle nearly closed, will suck exhaust back into the cylinder. You can actually feel this at the tailpipe, engine running of course, and assuming your system is reasonably sealed. Just put your hand over the tailpipe, not to shut it off, just to feel the pulses. When the bad cylinder comes around, it will fail to blow your hand off, and it will feel like it just sucked on your hand. Badaboom, you need a valvejob.

Now about that new ignition system..... Put a timing lite on her and watch the strobe-action, while you slowly bring the revs down from say 2000. The timing mark should smoothly move from an advanced number down to your base timing, without doing any stupid stuff; like adding strobes, missing strobes or seemingly jump the timing marks back and fourth.

Second last; check your timing-chain slack, by jockeying the crank back and forth against valve-spring pressure. It shouldn't move at all, but it always does. Just make sure it ain't more than a couple or so of degrees. If you find a lot od slack, AND the engine requires a lot of throttle to stay running, AND you have already changed the timing, it may be, that the chain has jumped.

Finally;
if your carb is puking gas, externally, it seems pretty obvious to me that the float valve system is not working properly, IMO you need to pressure test it.
However, if it is puking gas onto the throttle-blades at shut-down, and that gas is somehow finding it's way OUT of the throttle bores, that is a different problem, and points to the wrong gasket being installed during the carb-overhaul.