Adjusting the power to 2200 rpm in cruise meant I was unable to maintain height. So what does that tell me?
It tells you that the aircraft is not performing as it should. It doesn't tell you what causes that. As said, it can be an ASI malfunction, an RPM gauge malfunction, or an airframe that's somehow "dirtier" than normal, for instance because of a flap failure, failure to detach the tie-downs before taking off, a piece of cloth blown onto the tail, the previous pilot forgetting to remove the dead horse from the back, you name it. The aircraft we fly typically don't have dual-everything so there is no way to cross-check and *know* that a single instrument is failing.
Better find out what's wrong on the ground, not in the air.
And if you could not maintain altitude with 2200 rpm, why not limp home at 2550 (redline), which should give you about 80 knots? Why continue the flight over the redline limit at 2625?
Obviously if there was any other indication of the engine being outside limits it would have been a different story.
The next indication of an engine overspeed would most likely be a spectacular and catastrophic failure. A propellor blade detaching, a piston working its way out of the cowling due to a broken conrod, that sort of thing. But an engine overspeed doesn't lead to a gradual increase/decrease of oil pressure/temperature, which are the only other indicators that you'd have available.
So any single indication that's showing over the limit is reason to abort the flight, as far as I'm concerned.
I can't believe that you really want me to fly by RPM readings on final approach? Especially considering that all the evidence pointed to the tachometer reading incorrectly. I know it's possible to fly without the ASI on final, but honestly - air speed is absolutely critical at this stage.
What is the length of the runway you were flying from? Was that anywhere near the minimum required? Otherwise the airspeed on final, assuming a sufficient margin above the stall (no pre-stall buffet, no stall warner, no significant pull on the stick/yoke), is not nearly as critical as you think. That is, if you learned to land properly, bleeding off any excess speed in the flare.
Being PIC means having the privilege and responsibility of making a decision and standing by it. Sometimes with hindsight and more information one discovers that a better course of action could have been taken. Not this time!
So what you're saying is that next time you'll happily boost the engine over its redline RPM again?