Regarding Kanimbla logs: Based on research that I did for some NZ warships several years ago, my guess is that yes, the logs still exist and can probably be found at the UK National Archives, colloquially still sometimes referred to as “The Kew” (after its former location?). They probably won’t be available online, but you can try:
https://www.nationalarchives.gov.uk/ . Unless things have changed in the past few years, much, perhaps most, of the collection is not digitized, although they have digitized at least rough headings and descriptions of what they hold. Australia and New Zealand have retaken and/or digitized some of their records, so it is not always clear who has the records. Unless you don’t have a job that will pay you better for your time or have scads of time of time or if you just enjoy digging around for endless hours, I suggest you contact a private researcher. I’ll PM you contact info one who helped me get started and was competent and reasonable. If you want to try to find things for yourself, I’m afraid I can’t remember much, other than you’ll need to start in Admiralty 53.
You can also try the National Library of Australia.
https://www.nla.gov.au/ This won’t be easy either. I did a quick check of the Australia Joint Copying Project, and it looks like they have digitized some ships logs, but only for the period 1835-1892, which won’t help you. A simple search there didn’t show any logs for the Kanimbla. The NLA website has a section on contacting private researchers. The staff at NLA are very nice and might be able to guide you slightly over the phone, but they can’t do your research for you. If you go in person, they are more helpful than over the phone (at least they did about ten years ago).
Several years ago, I was able to find ships logs from summer 1937 for New Zealand ships Achilles, Leith, and a few others at the Kew. It wasn’t easy for me, although I think it would be fairly easy for a professional. I’m attaching just the first few pages of a log for the Achilles from July 1937 that I got at the Kew, just to give you an idea of what they look like. I’m guessing that they probably have something similar for the Kanimbla unless Aus and NZ were handled differently. The log will at least tell you where the ship was on given dates, but wont give a description of what they were doing. If you want a description of what they were doing, that might be in some kind of report somewhere, but doubtful it would to have been saved to begin with and hard to find if it were.
Just fyi, I heard from staff at the Butlin archives at Australia National University that some time ago they were getting in quite a few Aus Army patrol reports from WWII. Not sure if they would have anything for the Navy and/or pre-WWII or if they ever catalogued and digitized anything, but you might consider trying them if no luck with Kew and NLA. It would be a long shot though.
Good luck. I’ll do a separate post when I get time on my general thoughts about your project.