Thanks, astro. Maybe I will give the ND filter a go after all... But with 25% light transmission because less than that will also blur the image (I think).
ND filters are not very expensive and people who have used both polarizing and ND filters think the resolution of the ND filters is higher. I think that polarizing filters are mostly designed for daytime use, although they can also be used at night. It is just that the resolution is affected too much at night.
PS: Unfortunately without a filter the moon is too bright sometimes, particularly when it is close to full.