Loud pop and sputter on WOT? 68 318 Barracuda

AJ/FormS said
If she got unhappy at 14* advance, then something is most definitely wrong.
I'm assuming you set the timing with the V-can defeated and/or plumbed to the inactive at idle, sparkport.
If you say yes, then she should have been happier with up to 30*, idling in Neutral.
I highly recommend to verify that your balancer has not slipped and that the Piston TDC coincides with the balancer TDC. This is done with a piston stop.

If they are synchronized, then I would check the cam-timing.

Thanks for all the info! I will have to digest it. Pulled the plugs and photographed them. They probably have about 3,000 miles on them.

Yes, I set timing with the vacuum advance can unplugged, engine hot, and throttle completely closed. I do have the idle speed screw adjusted all the way out so the blades are resting on the transfer slot.