You keep using the term "choke". I know you are using it to mean like sputter, bog down, etc. but it got me to thinking. Maybe your problem is not a lack of fuel but rather too much fuel.
Also that click sound you describe...
Check the choke for proper operation. There are detailed descriptions out there - but simply stated: In hot weather - like conditions during the summer months in a southern state like Georgia - the choke should not ever even close. It is designed to close only when ambient is below 75 degrees F. And even then, it doesn't snap from fully open to closed.
The amount that it moves (from full open to full closed) increases with lower temps. If in proper adjustment, the choke plate should be fully closed if the air temperature falls to 45 degrees.
If it does close in hot weather, its no big deal really - it probably just needs to have the choke heater adjusted.
But having said that, let me add a qualifier: it's no big deal really - as long as it begins to open immediately upon start up of the engine and is fully open within a few minutes of engine starting.
The test is:
1. Remove choke coil from carburetor. After removal of choke coil, allow coil to cool to room temperature.
2. Connect a ``jumper'' wire between positive battery terminal and choke coil terminal assembly. Connect a second ``jumper'' wire between negative battery terminal and choke coil assembly grounding plate.
3. The tang on the choke coil should rotate 45°in 54-90 seconds.
4. If choke coil does not rotate or exceeds the 54-90 second time limit, replace choke coil.
5. If coil is within specification, check steps 1 thru 5 for possible cause.
If your choke is closing and not opening you may be running extremely rich.
Check it in the morning. Before you even start the engine - pull the cover off the air cleaner and look down into the throat. The choke plate is a single butterfly that is at the top and front of the carb opening. Without touching anything note whether it is open or closed (or some position in between).
Replace the cover, start the truck and drive your normal pattern. As soon as the engine starts to act up, pull the truck over (leave the motor running) Get out, open the hood and remove the air cleaner cover. Again note the position of the choke plate.
No matter what you found in the first inspection (the one you did back at the ranch) - by the time it begins to act up it should be wide open. Look at the second image I posted above. It shows a choke plate that is completely shut. If yours is like that after 30 minutes of running - it is way out of adjustment.
I don't mean to get your hopes up - but if it is any more than say 1/4 closed - you have most likely found the problem.