I can't offer much about the backfire other than your timing maybe off. What I can offer is my very recent experience with Pertronix and distributor issues. (See my other post)
First, do you have a full 12V to your Pertronix? In other words have you bypassed the resistor wire. You did not say which Ignitor you have, 1,2 or 3. The P3 MUST have a full 12V, but the earlier modules can run on resisted current (according to the instruction sheet), but are better with 12V. Your Coil may also be suspect as well if it's not a high output Pertronix. As for your Cardone distributor, I think you have the new one from Cardone Select that has the same slot as the Motorcraft Duraspark , in other words it is open and not just a hole as in the original dizzy. I would just "fix" this after placing the wires where needed by placing a bit of tape on the inside then using a dab of RTV to fill the top space, then remove the tape when cured. Also, the threaded holes are metric M4 (I think). If it's just a reman., threads should be 8-32.
There are many potential problems with the reman or "new" distributors that I was NOT aware of until I was forced to figure it out for myself. This could get very lengthy, but in brief is your timing correct, 34 deg no vac @ 3K? Do you get any pinging on acceleration? Is the vac advance set to add no more than 10 degrees?
In my case, I have a 71 351C 4V manual trans, so it will be a bit different to an auto set-up, but I needed to reduce the advance stop slot (welded it up and recut) to give me 20 deg on the crank, 14 deg initial and hardly any vac advance added. The new Cardone Select dizzy I have has an L15 slot, 30 deg on the crank. If you have 14 - 16 deg initial, then you would have 44-46 which for me was way too much timing.
Also, if you do have a Pertronix III (P3) I can tell you from experience it is a piece of junk. I sent mine back with a strong letter of complaint. Nothing wrong with the module itself, just the bad construction for the Ford distributor. It has a plastic sleeve/bearing between the two plates that is a poor fit, very loose and causes the rotating top plate to move laterally when vacuum is applied and the pick-up hits the cam lobes. I replaced it with a P2, no more issues.
There's a whole can-of-worms here, but while you may have vacuum leak issues and not timing causing the problem, I thought it worth going over as it has taken most of the summer for me to finally get a distributor that works. It took spending money to get it on a distributor machine to actually see what the problem was. Working in the car seamed okay, but was actually far from it. A timing light will only get you in the ball-park. I have found that today's distributors, remans or new are far from original spec and are "generalizations" that need work to get right, slots, springs, weights.
Anyway, I may have been going over what you already know, but others my benefit from my issues.
Good luck sorting it out and let us know what the cause was.
Geoff.
Edit: don't forget you still need a ground wire in the distributor between the movable top plate and the body when using a Pertronix Ignitor, 1,2, or 3