Before assuming there is still coolant getting by the head gasket, do some further testing.
Do check the oil for coolant. If there is substantial coolant in the oil, chances are it is still getting in, but might be from a cylinder oring seal. When the gasket was replaced, was the block and head thoroughly cleaned down to bare metal? Were the head bolt/stud/nut threads cleaned? The bolts retorqued once up to temperature? Were the valves readjusted after the retorque?
Depending on how long it ran, there could have still been coolant in the muffler/exhaust system still steaming out. That could have accounted for the grey smoke.
How is the spark quality? It should be able to jump 1/4" to ground at the plug end of each wire, not just at the cap or coil, but actually at the plug end of the wires. Check the point gap and condition.
As for the fuel system, is the tank clean? Take a fuel sample from the line at the carb with the fuel valve full open. If there is rust, dirt, water, the same will be in the carb and it may need cleaning again. Not necessarily another kit, just open it and clean it IF the fuel tank is contaminated.
Some things to check, the float condition, give it the "shake test", feel for liquid fuel inside the float. Look carefully at where the float swings inside the bowl. It must not touch anywhere. With the top cover upside down, gasket in place, set the level at 1 27/32" from the bottom of the float to the gasket with the float resting on the needle. To test the seat seal, holding the top upside down, suck on the fuel inlet fitting, put your tongue over the hole. If it won't hold vacuum, there is a leak somewhere, bad needle valve, loose seat, bad gasket...
Look at the throttle plate fit in the bore. With the idle stop screw backed out, the plate should seal completely tight to the bore. The edge of the plate is machined to only fit one way in the bore. If it's installed incorrectly or not centered in the bore, it will not idle properly.
Before reconnecting the fuel line, (after the tank has been cleaned or checked and proven clean, the sediment screen in place) open the fuel valve and flush the line. This gets all the trash out of the line. It only takes a tiny speck to hold the needle valve open.
With the line connected, fuel valve open, the carb should now be successfully holding fuel without dripping. (Dripping following a failed start is normal).
Before going further, review everything needed for the engine to run properly. There must be good, even compression, proper valve lash, good spark, properly timed, a working thermostat installed, oil level correct and clean, free of gas and coolant, and the air cleaner properly serviced.
The start up! The initial carb settings are one turn of the seat for the idle mix screw, 2 1/2 turns off the seat for the main jet.
Start the engine, run it up to operating temp.
If the head has been back off, retorque the bolts and adjust the valves again before proceeding with the carb adjustment.
With the engine up to temperature, set the idle speed to 450-500RPM, no higher. Turning the idle mix screw out leans the mixture. The range is very limited, but it should make a difference in idle quality. Back it out until the idle shudders, then back in to best idle, then slightly rich.
To set the high speed jet, open the throttle suddenly, listen for the response. Start turning the high speed screw in 1/4 turn at a time until the engine stumbles on acceleration. Then back the screw out 1/4 turn at a time, repeating the test until it will smoothly take sudden throttle without hesitation. A single puff of black smoke is the goal.
