exhaust backfire

So what next? I think it would be near impossible to do that leakdown test on a hot engine (getting around those 2" primaries when they're hot, burning my hands, melting the leakdown tester hose, etc...)
It is possible and sorta easy but a royal PITA.
But before you start, isolate which cylinder(s) are doing it.
Then, just dismount the valve gear and do the LD with the pistons at the bottom. If you get a funny number, you can bop the valve stems with the wooden end of a hammer handle, to see if the result changes. If you have a leaker you will hear the difference as you are bopping and see the numbers jump around after each bop, usually leaking less each time.
But honestly, I kindof don't think the problem is in the LD.
I'll tell you why;
As kids we used the motor down the road,with a manual trans or an automatic with a rear pump, and shut off the ignition, with the trans still in gear. With the key off, and the engine being motored by the rear wheels, this would fill the exhaust system with a highly combustible mixture.
And then when we would return the key to "run", the first flame into the pipe would light the whole thing off like a cannon. The mufflers didn't always survive.
I think, by your description, this is what is happening to you, just don't know how.
I would think it starts with a misfire, and a fuel charge passing thru the chamber unburned. Actually I guess it would have to be a string of them, to accumulate that much mixture in the pipes or mufflers.

I'd like to know which cylinder(s) is/are doing it.