Just a guess:
You may be running too rich. You say you staged it one step richer already, maybe that was the wrong way to go.
If you say all Vac lines are good and the timing is right with new plug cables, cap and rotor, then I guess it wouldn't be crossfiring either, and therefore probably not a timing problem.
If it runs well otherwise your valves will probably be set OK.
That leaves fuel-related problems as the quickest to find: If it pops through the carb it's often the ignition set too far advanced and the spark ignites the fuel before the intake-valve closes. But you say it's popping through the exhaust. If I were you I would try the following: see whether you can find out if it always pops through the same side or if it changes sides. If it only pops on one side it might just be a wrongly set ex-valve.
But if your running too rich (and the mixture gets even richer under high load, because of the little accelerator pump in the Edelbrock carb) you might be getting too much unburnt fuel out into your hot exhaust pipes. These get even hotter under load so it might just be enough to ignite some vapors here and there. That'll give you the popping (backfiring). A giveaway for too rich mixture is poor mileage (but not only that). Try to find out whether your exhaust vapors "smell" of fuel (be careful doing this and don't take too deep a breath, but if you just stand behind your car and smell, you ought to be able to detect a smell like you get at gas-stations). That would also mean your running too rich. If all this doesn't appear to be the case, your problem might be elsewhere, as I say, I can only give a rough guess with your info.
If you do think this might be the problem get rid of it the following way: get some carb-jets and rods (very easy to swap in an Ede and hardly cost anything) and go 2 steps leaner than you are now (so one step leaner altogether) in the power mode. Check if it makes a difference. While your about it, check your float height (easy to follow instructions on how to do so are on edelbrock's site under technical support).
I think that will be the cheapest (and possibly right) way to start tackling your problem. If all this doesn't change a thing your out of 20 bucks max and an hours work. Cheaper and faster than checking your timing chain...
What happens if you go up a slope and accelerate slowly?
What happens if your stopped, in gear (level ground) and kick it?
What do you have to do exactly to make it pop?
Just my few cents worth...
Let me hear how you're getting along,
Max