what grade is the oil?
i run semi synthetic 15-40 in mine and my oil pressure is always stable, always is a bit lower at idle then under acceleration but that's how it should be.
then again i change it every 5000 km.
only thing i can suggest is to change and save the oil and see if there is any difference, better that then creating a leak with too thin oil or burning it and glazing the bores.
thats just a suggestion