First i'd do a visual check to see what is happening on #6.
With the engine off, look inside #6.
Activate de linkage to see if the throttle plate on #6 is moving or not. (#3 and #6 are on seperate shafts and linked with the 2 other barrels on the carb with small allen bolts. 4&5 might be opening but #6 might stay closed.
Also activate the linkage to check if the accelerator pump jets is squirting fuel. Might be a good idea to measure the volume of fuel from the accelerator pump jets to make sure they are identical from side to side.
As for the the popping issues it appears to me that you might be lean on idle. i'd check the size of the idle jets. Any idea how many turn out you are with the idle mixture screws?
On my engine when I ajust the carbs (while turning in the idle mixture screws) , there is a point where i can hear it poping in the exhaust, just before loosing the cylinder and having the rpm drop.
You can check the idle circuits with the engine running. By turning in the idle mixture screws, slowly by increment of 1/4 turn and waiting about 10 seconds for the engine to react, you should loose that cylinder or at least have an rpm drop. If nothing happens and it's fully turned in, back it out completely. If nothing happends then the idle circuit is blocked somewhere.
http://www.pelicanparts.com/914/Parts/914-6/914-6_weber3_big.htm
shows a nice diagram of the idle circuit. Mine had theidle circuit blocked on 2 barrels in the 22 passage.
HTH
Marc-Andre Morin
70 914-6 conversion 3.0L Webers