Taking bets on what's wrong with my motor...

I think he's also got the firing order wrong. If you've wired it 15426378, then try 13726548. Pertronix could be damaged, the Pertronix I I had would pop and sputter after a backfire thru the carb. Had to shut it off and restart it to clear it up most times. Check also the valve lash, too tight a setting here will also cause rough running. Pull the plugs and examine them one by one. I had a rough running 400 that turned out to have a closed spark plug gap, from the heads getting bumped around while the motor was disassembled.
 
while you're at it, the backfire may have roasted your power valve in the carb. Probably not the main cause of your problem, but that cam won't give you a lot of vacuum and you are probably dipping into the power circuit at idle. I still think your main problem is ignition though.
 
The part number for the cam is 31-246-3. I adjusted the lift figures for my 1.6 rocker ratio. I called comp, and they verified that it uses the original 289/302 firing order. If my cam had been part# 35-246-3, it would have used the 351W order.

All of my header primarys are hot, so all cylinders are firing some of the time.

I've already eliminated plugs and wires as possibilities.

There is no power valve in an Edelbrock carb.

When I finish getting it back together, I will check the plug gaps, and swap out my distributer. I will also hand roll the motor for a final verification of the cam's firing order.

I'll also take care with the valve lash.

Thanks for the input everyone.
 
your timing chain might have been off and skipped a tooth, and the distributer/cam might have eaten a tooth on either at the point where they meet. this caused a similar problem on a friends 429. And as others have said, backfires themselves can cause other damage, so your pertronix/carb might need a look. But yeah, my money is on the gears connecting the dist. and the cam and the timing chain... the cam itself might be fine, but that doesn't mean the gears are okay.
 
The timing chain and gears were in great shape and lined up perfectly (it's a new double roller), and the distributer and cam gear teeth are fine as well. I checked all this when I pulled it apart.

I am leaning towards the petronix being on the fritz. I will be able to eliminate the carb as the cause once I get it back together. I have another edelbrock off another car on the shelf I can swap onto mine.

I'll also inspect the distributer base and housing for play and sticking (it's a stock 68 distributer with the petronix installed).