Missing a shift can do a number of things. Bending a valve is one thing. Sometimes the piston is damaged, but I don't think a either of those would cause a misfire. Sounds more like something is damaged in the ignition or fueling system. To be honest, the base RSX motor and the Type-S are 2 totally different beasts. Similar blocks, but the closest thing to the base engine is the EP3 Civic Si (aka a runt of a Honda motor). You'd really be best off finding a K20A2, which will solve all your problems and give you lots more power. This would be a direct bolt-in, and if you get everything off the junker engine, then putting it in will take no more than a weekend. You will probably need a new tach for the new engine, and the Type-S shifter (so reverse will work correctly), but everything else you need should be attached to the engine. And make sure you have very solid paperwork for your new motor. You will have to take the car to a dealership to get the ECU programmed to work with your key. If they have any doubts about how you got your new engine (ie they think it's stolen), they won't do the reflash. And while your old ECU will run the engine, but don't expect it to handle the VTEC. That's just asking for another dead motor.
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"I really like going fast. Just go off and meditate in the wind, you know? As corny as it sounds it works and feels good. It's a good way to just let the weight of the world off every once in a while...is this a big pose? I mean, yes this is a pose! I mean am I driving down the street to not get noticed in this thing? I mean rebellious is what this thing is I would say!!!" -James Hetfield

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