I'm not exactly sure why, BUT how much visible fuel might be in the "clear" fuel filter is NOT a real good indicator of fuel going to the carburetor. Reason? When our '66 Newport 383 2bbl Town Sedan was newer, I felt it was better to have a fuel filter that was "clear" so I could see what was going on. This made sense to me, rather than the shiny metal filter that Chrysler used OEM.
BUT, what I noticed over the decades I drove the car (we still have it) is that in some situations, the filter would appear empty, yet the car ran great and fuel was obviously getting to the carburetor, not vapor. So, do NOT use what you see in the fuel filter as a good guide of what's going through it to the carburetor. This was what I saw happening over 140K+ miles of use. I have no explanation as to how this all happened, I just know that it did. I suspect Chrysler Engineering did too, which was probably one of the two reasons they used the full-metal case fuel filters.
As to the starting issues after the engine is warm . . . ONE thing to do is to make sure the complete ignition system is as good as it can be. Spark plugs in good condition with a gap between .035"-.045". I personally like NGK V-Power plugs, or their fine-wire Iridiums, for getting the spark exposed to more air/fuel mixture and a better burn. Make sure the rest of the ignition system is in good condition too. Having the timing at OEM specs (CHRYSLER specs, not what some associate might recommend) is a good baseline to which to start with. More on this later.
If it runs good after it starts, things usually are pretty good. Use about 1/3 throttle when cranking the engine, as that seemed to always work best for me with multiple carburetors (2bbls, Holley 4bbls, etc.). This is also inline with what the Owners Manual for the '66 Newport suggested (1/3 to 1/2). That setting has worked well with the fuels of earlier times and the progression of fuels since then. At least here in TX, as there ae something like 15 different fuel blends/specification that Exxon-Mobil makes for the USA. Which means that "E10" might be a national level of ethanol, BUT that does not mean tha fuels in TX are the same exact blend you get in your locale.
Learn what the CAR likes, not what you perceive it should like. This is one of my orientations such that "the equipment" and myself learn to get along together. Each car can have it's own personality differences, so learning them is important.
As to fuel smells, you need to determine if there are active leaks in the fuel lines/fuel pump/rank, but ALSO be aware that other factors can be at play here. Is the smell strong or just some evaporating vapors. The carburetor float bowl is open to the atmosphere, as the fuel tank is also vented to the atmosphere. Not a closed system as modern cars have.
How NEW are the fuel lines? Not just what you might see under the hood, but all the way to the tank. There is a short section where the fuel tank sending units meets the undercar line (with a special clamp that grounds the fuel tank gauge unit) and another small section at the rear of the stub frame, before the line gets to the rubber lines on either side of the fuel pump, and then the final section where the fuel pump is. IF there are any questions of their age, REPLACE THEM. Ethanol is a solvent and will degrade the rubber from the inside out, as the outer surface can still look decent, but can fail suddenly with possibly the outer layer of rubber falling off to reveal a seeping inner fabric reinforcement layer. As fuel evaporates, looking for these things before the fuel evaporates is important to finding them.
As to the carburetor, make sure the idle is set to "lean best mixture" and not too rich. I would also recommend a thick, OEM-style base gasket to keep the carburetor cooler. Edelbrock and Holley both sell them, as well as NAPA and other places. Might need to order them, though. About 3/8" thick, with plastic or metal bushings in each of the carb mounting stud holes, so only a certain amount of compression of the gasket happens. It might not be production correct, but it is just another effort to keep the carburetor cooler, as I have found out, too. There are versions which have 4 holes in them and some which have an open area under the carb. The 4-hole version might work better, but either one will work.
Ignition timing? Start with OEM specs and if there is no pinging on on-ramp part-throttle acceleration, you might try advancing the base timing 2 degrees or so. Then re-check WOT For pinging, too.
Understand, too, that fuel refineries are transitioning into "summer gas", which means the more volatile "winter gas" might still be in some stations' tanks. More volatile gas in higher-than-blended for ambient temperatures means it evaporates easier, which also means it can be more prone to percolation in a hot engine, when the engine stops and any fan air flow over the carb and engine stops. What's on top of the engine? The carb and air cleaner. So, fuel can get hotter in the float bowls and evaporate out, causing some "smells". Check for leaks first and then learn what might be normal in this respect.
Your carburetor might be new, but check the actual adjustment of the automatic electric choke. At an ambient 70 degrees F (ambient meaning EVERYTHING under the hood is at that temperature, not just the outside temperature), adjust the choke coil to just lightly close the choke plate. Check to see that the car starts and runs good there. That will mean the choke opens as soon as it can for best operation "as lean as it can". Then adjust the idle speed to 600-650rpm with the idle mixture screws adjusted for "lean best idle" using a tachometer only. Check the ignition point dwell if a points distributor is in the engine. No adjustment for an electronic system. Then set the base ignition timing. See how it all works, as a baseline, and then tweak from there to ensure things are as good as they can be.
Is the intake manifold stock cast iron or aftermarket aluminum? Just curious.
Sorry for the length, but I detected you might need some explanations on things.
Please keep us posted on your progress,
CBODY67