That is a standard GM carb, the only filter is what you pulled out. No filters inside. There may be a piece of something you are seeing so try and pull it out. Again, no filter or screen inside the carburetor!
This is the type of filter it could have,
https://quadrajetparts.com/sintered-bronze-carburetor-fuel-filter-p-80.html or this type,
https://quadrajetparts.com/short-paper-carburetor-fuel-filter-with-check-valve-p-79.html . The screen you pulled out is for marine use or racing.
Headers pipes thin with age from heat, so your problem could be a combination of low voltage and heat soak. One place to check for voltage drop is the large bulkhead on the firewall with all the wires coming out, the engine harness unhooks from engine side. I have seen more then one have a bad connection.
A semi easy test is to attach a heavy wire to the ( S ) terminal on the starter solenoid, ( while engine is cool ) and secure it close to the battery but not touching anything. When the truck won't start, touch the wire end to the battery ( with key in RUN ). This will bypasses all wires, connections, and key switch, if it still does nothing, you are down to heat soak or low BATT voltage to starter.
As a side note, running lean will dry out the spark plugs, they should be pretty clean and colored. I have seen my 250 inline 6 run 700 to 900 degrees about a 16" from the exhaust valves, measuring the down pipe while driving.
