Needed: Advice from a Slant 6 Master!

You need to verify if it's fuel or ignition related, or even a mechanical problem. You can't just assume carburetor problems from the seat of the pants driving. Your gonna have to have some tests done.
Some suggestions might be; Is it points or electronic ignition? Worn points will cause backfiring & hesitation/ stumble. Check the gap & dwell of the points. Make sure they aren't burnt & the rub block isn't worn too much. You also need to verify good electrical connections throughout the ignition system. What did the old plugs look like when you took them out?
Fuel pressure & volume must be consistant. Fuel pressure gauge needed along with a container to check volume. Is the choke operating correctly? Fully opened when warm?
If ignition & fuel check out, then you have to start checking mechanical condition. Compression test, cylinder leak-down test(preferred), valve timing, vacuum leaks etc. Intake manifold bolts tight? Carb getting too hot -vapor lock?
What did you adjust the valve lash to?
Without seeing the car 1st hand, I'd probably start by checking the point/ ignition 1st, then go fuel then mechanical.
It may seem like more work initially, but you'll save a lot of time & certainly money in the end.