I replaced the engine in this 2009 Subaru Forester and started having P0303 and P0304 codes during hard acceleration. I followed guidance from several people on forums and eliminated options such as spark plugs, plug wires, ignition coil, oxygen sensor, and off timing as possible causes for the phantom codes that would cause the engine light to illuminate at around 5000 RPM and show cylinder 3 and 4 misfire. The engine sounded fine and ran smooth, so my concern wasn’t that there was an actual misfire, but some little flukey thing. The solution ended up being the crankshaft pulley that drives the timing belt. Although I could not see a defect, it had to have been off balance with a bent tang or something, because once I swapped a different one in its place, the codes disappeared!
Here is a link to a Forester thread that guided me to try this as a last resort:
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