You seem to have checked all the right things (electronic) You are inside the laid down recommendations and I hope all goes well for you.
At those speeds you should notice a real improvement (assunming the RAM is adequate).
The mechanism of replacement is easier once you have done it! I would recommend gentleness and cleanliness.
The retaining clip may be stiff but the CPU should almost drop in. Clean off any thermal paste remaining and use the new stuff sparingly. Metal to metal contact is the ideal, but the paste is there to fill any tiny air filled gaps and give best heat tranfer possible.