I can’t answer your question either but I have a two-blade SR-20 that I’ve flown for over 500 hours. I’m based at a Bravo-airspace airport and shoot many ILS approaches, some in IMC. As a practical matter, I’ve never experienced CDI needle oscillation phenomena. A “normal” approach for me is to intercept the localizer at 23" of MP then 17-18" at a dot-and-a-half above the GS (50% flaps) then 13" at the DA if the runway is in sight (100% flaps). I have to admit, with the automatic prop speed governor I’ve never looked at the prop speed on an approach but I’m guessing that the prop speed should be below 2,600 RPM at the MP’s I use. The only time the prop speed should exceed 2,600 RPM on the approach would be going missed. Once I got the plane configured for the missed I’d fly the GPS to the published hold or follow ATC’s instructions and wouldn’t leave the GPS on the “LOC” setting.
Thanks for your question. I hadn’t thought about the RPM issue before. I’m going to check it out the next time I fly a localizer…