Surging and Backfiring

350 SBC Chevy with a new Rochester Q Jet Elec choke. Fuel press @ 5lbs, idle enrichment screws each 3 turns out. Engine starts but surges and will occasionally stop. When I activate throttle quickly, engine backfires. Left to idle, surge returns. Moving RPM up more slowly, engine runs fine during acceleration but holding steady at say, 3000, no surge. Anybody got an idea ?

Sounds like more than one problem with the carburetor. Rebuilt carb or what?
The problem with hitting the throttle quickly sounds like an accelerator pump problem. The surging and occasionally stopping sounds like a problem in the idle and off-idle circuits possibly due to a clog or restriction.

There are other things such a badly worn throttle shaft bores, improper ignition timing, vacuum leak, leaking jet well plugs, or EGR fault (if equipped) that could cause surging also. No details on the 350 though as to year, model of vehicle, etc.