Ok, well after exhausting all that I know about trying to fix my problem (replaced the fuel filter, fuel pump, checked the points, checked plugs, wires, checked for vacuum leak, etc), I gave in and took the truck to a mechanic.
I had at least isolated the problem to the carburetor, and in fact the problem ended up being in the carburetor.
The official problem was a clogged "idle circuit".
The mechanic told me the "idle circuit" tube is about the size of a hair. He said it's very easy to clog.
He suggested in the future if that happens again, to pull the idle screw all the way out and blow air, or carburetor cleaner into the hole.
He ended up rebuilding it with a rebuild kit while he had it apart.
I don't know a whole lot about carburetors, so today was a $360 learning experience.
Thanks again for everyone's suggestions above.
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Monkey Truck's post in Slight backfire and engine stall was marked as the answer