My 1958 Johnson 18 had missing & backfiring when I bought it too. Many items already may very well be the problem but was the magneto seem covered with oil. My top seal had gotten very hard & not sealing very well spraying oil on the magneto. With your needle jets not staying snug you also may have a vacuum leak causing the motor to run in a lean condition causing missing. Have you removed the spark plugs to see how they are running? Should be a dark tan to be running correctly. Please try to get the missing repaired as it causes the motor to be out of balance. Let us know how you do.