As Paul has indicated, only the 3.4L engine in the 987.2 series had the DFI engine with a high pressure fuel pump Graham, so you can discount that as being a source of your problem, although a pump of some kind could be a source since it seems as though it’s a constant frequency, which would rule out anything engine-related like ancillaries.
Definitely I reckon that it would be worth trying a nitrogen fill for the tyres, the rears at least. It shouldn’t be too expensive and I’m sure that you can find a tyre shop in your area which offers the service if you look online. For context I think that Lexus was the first manufacturer to use it for their first car, the LS 400 which was noted for its refinement, and maybe in part to overcome an NVH issue. If it doesn’t work then I guess that a tyre-related source would drop down the list of possible sources even if it couldn’t be ruled out completely, and a nitrogen fill has other benefits including a more consistent tyre pressure with temperature and better pressure retention.
Jeff