Whoa, whoa, whoa. Before we jump off the rails fretting about things like timing chain tensioners, and taking the motor apart, let's use our heads a bit.
Have you checked the header bolts, to be sure everything is tight and there are no leaks at the flange?
Howzabout lifter preload on the exhaust side? Could you be a little tight? No sense taking anything apart until you try loosening up the exhaust adjusters a quarter-turn, to see what happens. That can easily be causing the popping in the exhaust. Do you own, or have access to a leakdown tester? If so, bring the motor up to operating temperature and start leaking it. If not, regulate an air line down to 100 PSI and use an air hold fitting in the plug hole. Bring a piston up to TDC, screw in the fitting and add the air. Do you hear air escaping into the exhaust?
What color is the exhaust? Black? Gray? Dark-gray or very light? It is actually pretty easy to get so far off on fuel mixture that an extremely lean motor will start acting like it is rich. Same with an extremely rich motor wanting to act lean. If it is too lean, then there is not enough fuel to support combustion. If it gets too rich, you'll wash out combustion. Either way, you can still end up with unburnt fuel collecting and burning in the exhaust. A motor can be a bit rich and have a loose header, which introduces enough air into the hot exhaust to start burning in the header. Don't get carried away with bright lights, magnifiers and counting hot threads, but pull some plugs and see what they look like. Let's try to get an idea of what the chamber environment is like and then we can move on from there.
I'm guessing this is an even-fire motor? Un-common rod pin crank? If it's a common pin crank, be sure you are running the correct distributor and cap. The 90°/150° combination will actually try to run on a 120° ignition, but not well. Most V-6 caps are flaky, with long leads in the cap, so they can work with either combination. Try pumping up the secondary side of the ignition and you're inviting problems in the door. We modified distributor bases to accept a Volvo cap, which had the correct 90°/150° spacing. (SM, do you remember the V-6 cam trigger ignition Mallory used to catalog? That was actually our stuff.)
Francis, it sounds as if you're experiencing a lean backfire. Is it doing this with the engine warmed up, or are you trying to rev a cold motor? This one could be as simple as the motor needing some more choke. Until we get some more evidence presented, it sounds like you have two distinctly different issues.
Call me lazy, cheap, or whatever, but I always like to try the really simple things first. You know, the stuff that requires minimal effort and zero dollars?
Of course, you can always pull off the radiator cap and drive a new car underneath it, but I would get some tools out before I got quite that carried away.
EDIT - We posted atop one another. Never mind my suggestions.