"Its never the carburetor."
I know y'all were waiting for this...

To the OP, I need to have t-shirts and hats made which state the above quote.
Personally, I always leave the carburetor for last when troubleshooting, unless fuel is pouring out of it.
In your case, it seems to me that you're having two separate problems at the same time. You found one of them. The carburetor.
Now you need to leave the carburetor alone and find the other problem. This requires a vacuum gauge, a compression tester, and a multi-meter.
Since you didn't mention that the engine dies, I don't believe that you have a fuel delivery issue.
This leaves ignition, compression and vacuum leaks.
Test all components involved in each of these areas.