A rebuilder can install bushings around those throttle blade shafts to stop the leaks, but that's an expensive proposition. I'm betting $300 and up to redo the carb.
Still, I don't see how a slow drip from that area could make your car run the way it does. Presuming your uncle knows what he's doing, I still think ignition is the problem. Suggestions
*Recheck spark plug wire firing order. 1-8-4-3-6-5-7-2. I had a friend, Pete, come over to tell me the truck I sold him was missing (skipping). Pete's not stupid, but I saw new plug wires. He had swapped wires on adjacent spark plugs. Truck ran fine after we fixed that.
*Check that input voltage to the distributor is near 12.6v (battery voltage), ign key in Run position, distributor connector disconnected. Distributors do weird things when underpowered. If underpowered, somebody else rewired that car for points. No telling what they did. It's a matter of following wires and finding out.
*Check the wire that the distributor uses to ground the coil, from the distributor connector to coil negative. That wire can't have much, if any resistance. Replace that wire if it has more than 5 Ohms resistance. It really should be zero or very close to it.
Note: none of these checks costs anything and replacing wires costs very little.