If that car is shutting down at the high rpm, a jet kit may only make the problem worse? A properly jetted set of carbs is a key to a great performing engine but you also need a good supply of fuel. If you increase the jetting (richer) you will use fuel faster and run out of gas sooner possibly? You may want to ask around and see what everyone else is running for a fuel pump, fule lines, filters etc.
Also is the fuel filter old?
If it is plugged you will restrict fuel as well. If your fuel cell is old and has old foam that can plug the filter as is breaks down from age.
A lean burn would make your car run hot, a extremly lean burn will make it run very hot and ruin the engine.
Dont get me wrong on this, a jet kit will make good carbs better but be sure that there is no other problems as well.