at any MAP above about 18-19", the governor should start controlling the rpm. 2400 with prop at full fine sounds low for a TIO540, but I will take advice on that
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It almost sounds like the governor is holding in a too coarse position hydraulically, and not letting the prop settle on the physical fine pitch stop - easily caused by poor adjustment of the propellor control teleflex. Once the MAP is insufficient to drive the propellor into CSU range though, the prop will sit on the physical stops no matter where the control is set. If you come in with 2200rpm set, but reduce MAP while S&L until it can no longer maintain 2200, it will just drop away with airspeed (if maintaining S&L though). As soon as you increase power again, if you haven't touched the prop control, it will re-govern at 2200rpm again.
What RPM can you achieve in a dive? would be interesting to see if it held 2400 or climbed through it. Remember the governor is controlled by flyweights inside it - driven by prop rpm. all you are doing is setting spring pressure when you adjust the prop lever, and if you accellerate it in a dive, it should still govern to the limited prop rpm