As others have said, you were seeing gas percolating out the discharge tubes in the booster venturris. If the engine was fairly warm, the gasoline in the float bowl was boiling and the vapors were condensing in the tubes and dripping into the venturris. A heat isolator plate might help a little, but will do little for heat soak, as underhood heat will affect the carb regardless. This has always been the case with carburetors, but perhaps is worse with todays gasoline blends. Modern cars with fuel injection and electric underhood fans have made us forget the "good ol days" of carbs.
Check the float level as sugested, set as per the factory service manual (post your carb # maybe somebody on the board can give you specs). As for letting more fuel into the engine goes, why do think it is too lean? Unless you have a major lean-surge, I would think twice about arbitrary carb mods.
OK, so your ignition system is 110% and you want to play with the carb. Step one would be getting a rebuild kit, thoroughly cleaning the carb, and reassembling with new gaskets (and pump). Set everything as per factory specs. Also note the #s of your primary jets (front), secondary jets (rear), and metering rods. Put the carb back on the engine and live with it for a day or two. Next step would be changing needles 2 numbers smaller. If that makes a HUGE difference, then you were indeed lean. Little or no difference would suggest you were pretty good to begin with and will likely just wreck fuel mileage.
Remember that most "fuel" problems are ignition related. Also, too rich a mixture will cause most if not all the same symptoms as too lean. Without knowing your combo, it's really hard to make any sort of suggestion besides making sure that everything you have now is working properly before you go making changes.