Sean:
I'm new to C10's as well. I recently bought a 63 short fleet with a 230 inline six. The description of your problems mirrors mine. I had a persistent stumble when I hit the gas and it was very unhappy when cold. My engine was pretty much stock, though the original Rochester Model B had been replaced by a Rochester Monojet. Here is how I attacked it:
1) I replaced the distributor with an HEI unit from 12bolt.com The reason I chose them is they actually put the distributor on a machine to check the advance curve. Replacing the distributor did little to solve the stumble. I made sure the timing was right (vacuum, centrifugal, and initial) including checking that the timing pointer was accurately indicating TDC. The new distributor did little to change the stumble and cold performance even with ideal timing.
2) I pulled the intake and exhaust manifolds. I knew my exhaust heat valve was frozen open and the gaskets were leaking. At the same time I purchased a "restored" Rochester Model B carburetor from Daytona Parts. (Their work and advice were fantastic.) After freeing the exhaust heat valve, cleaning, and putting everything back together, the truck runs really, really well.
In my case, the issue was most likely the carb, though several items were addressed during the carb install. Specifically, I believe my stumble was due to a bad accelerator pump. (It should squirt as soon as the throttle is moved.)
Regards, Cris