Misfire/backfire

Hello - I experience missing and sometimes "backfire" (like a popping that seems to come from the exhaust) mostly evident on sudden acceleration. My mechanic noted that P0300 code was present and he cleared it. He also found low fuel pressure and replaced fuel pump and filter with no change in the condition. In driving around to isolate the conditions when it occurs, I find that it will almost always miss and pop when I mash the throttle. However, if I accelerate steadily it can get up to 4,000+ rpm without a problem. Idling and low throttle driving is mostly perfectly smooth. Sometimes it will show up pulling away from a stop, but backing off and then slowly rolling on the throttle stops it. When I check for codes now on the odometer I only get 55, which I think is normal. Does these details help to point at a likely cause? - Steve