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If the backfiring only started after changing the carb adjustments, then I think the distributor is not causing the problem. But it is very important to ensure proper ignition timing before adjusting the carb. So make sure to check the timing, and inspect the distributor. The timing must ALWAYS be proper before attempting carb adjustments. Improper ignition timing can cause backfiring, but so can mixture problems. Take the cap off and wiggle the shaft to see if it has excessive side to side play from worn bushings. Excessive wear could cause inconsistent timing. Replace the distributor if you feel it is beyond repair.
Using the vacuum gauge is a good way to diagnose. Take a look at this page for some good carb tuning info and what the vacuum gauge can tell you:
Use a vacuum pump to test the vacuum advance diaphragm for leaks, and watch inside the distributor to see if the vacuum advance mechanism works without binding when the vacuum is applied and released. If the advance sticks in the advanced position, it can cause backfiring.
The backfiring was probably initially caused by the mixture being too lean. When I was explaining about changing the power valve, I was trying to make the point that the carb could have been adjusted to compensate for extra fuel from a blown or wrong-sized power valve. Therefore, the jets might have been already on the lean side since there was additional fuel all the time from the (possibly leaking) power valve. Once you changed the power valve, the mixture was probably leaner, but then it was leaned further by the jet size reduction. It might have needed no jet size adjustment, or an increase in jet size.
The backfiring can cause the power valve to blow out again on oldercarbs. Holley revised the design on the new carbs to incorporate powervalve protection by means of a spring loaded check ball. This type ofprotection can be added to older carbs with a kit that costs about$10-15. The easiest way to check for blown-out power valves is togently turn the idle-mixture screws all of the way in. If the enginestarts and idles without stalling, it's getting fuel from somewhereelse—most likely a leaking, blown-out power valve. Or too much of thetransfer slots are showing like I explained previously. I recommendchecking the power valve again, and going back to the jets that wereremoved. It might be necessary to go to further tune by additional jetchanges. Check the power valve, install the protection kit if your carbdoesn't have it, and switch jet sizes to a larger number, then see howit responds.
Since the backfiring changed from intake to exhaust, I wonder if you have the original exhaust system with the Air Injection Reactor system to reduce emissions by injecting air into the exhaust. There is a diverter valve in the system that is vacuum controlled, and it is designed to stop airflow into the exhaust on deceleration to prevent exhaust backfires. Air leaks in the exhaust can also cause backfiring. If the diverter valve diaphragm was damaged, it could be allowing air to pump into the exhaust. Disconnecting the air pump would helps diagnose if it was pumping air into the exhaust and causing the backfire.