I have a 2000 Accord 3.0L Vtec 268,000 miles that has an intermittent problem. It usually occurs when engine is hot. The engine will cut off while idling and is very difficult to start. Sometimes it may start when I hold to gas pedal to the floor, then it will run smoothly when maintaining about 1000 RPM. If I try to let it idle, it will cut off. When driving it, the engine seems to run as if nothing is wrong and has strong acceleration, (but will cut off when I let it idle), then some random time later (15 or 20 minutes) it idles and starts fine as if it never had any problem.

Most recent engine codes when scanned with my cheap scanner:
P0301
P0302
P0304
P0305
P0306
P0300
P1399
P1457

Parts that have been replaced:
All 6 spark plugs, all 6 coil packs, fuel pump, fuel pump relay