I just had the exact same thing happen to me.....backfiring through carb after a rebuild, wouldn't start no matter what I did, adjust valves, set timing, new distributor, wires plugs, new heads, rebuilt carb, no intake vacuum leaks, good compression, plenty of fuel, spark and great oil psi. NOW for the trick. When I took the crank out, and rebearinged the bottom end, one thing I should have checked for which I didn't and here it is:

The jerk who owned the 350 I bought who had put a brand new double roller chain in it.
He was a dogkrapface and did not find TDC when reinstalling the crankshaft timing gear.
At TDC I had the arrow on the gear facing up, not the circle.
Then when installing your timing chain, you think everything is ok but it is not.

Circle to circle was NOT tdc on number 6(cam circle at 6 oclock crank circle at 12 is TDC on # 6)( cam circle at 12 and crank at 12 is tdc on # 1.

So by him not installing crank gear correctly, and my own stupidity for assuming he did, when adjusting the valves, I was and you are actually on the ramps of the camshaft and you will never get the valves or the timing correct.

I took the cover off, ripped down the front of motor, removed chain and gear, found TDC #1 reinstalled gear and chain with circle to circle(TDC#6) then rotated engine so circles are at 12 and 12 for tdc#1, dropped in distibutor etc etc, set valves normal way when all back together, with timing set at 8 btdc, it fired immediately not even a crank. All backfiring gone, running incredible.

Moral of the story, dont second guess yourself, just double check yourself, hope this helps.( rotate to TDC#1 THEN install crank gear with circle at 12)